1. A car got [latex]33[latex] miles per gallon using gasoline that cost $[latex]2.95[latex] per gallon. Approximately what was the cost, in dollars, of the gasoline used in driving the car [latex]350[latex] miles?
(A) $[latex]10[latex]
(B) $[latex]20[latex]
(C) $[latex]30[latex]
(D) $[latex]40[latex]
(E) $[latex]50[latex]
2. Working alone at its constant rate, machine A produces [latex]k[latex] car parts in [latex]10[latex] minutes. Working alone at its constant rate, machine [latex]B[latex] produces [latex]k[latex] car parts in [latex]15[latex] minutes. How many minutes does it take machines [latex]A[latex] and [latex]B[latex], working simultaneously at their respective constant rates, to produce [latex]k[latex] car parts?
3. Machine [latex]R[latex], working alone at a constant rate, produces [latex]x[latex] units of a product in [latex]30[latex] minutes, and machine [latex]S[latex], working alone at a constant rate, produces [latex]x[latex] units of the product in [latex]48[latex] minutes, where [latex]x[latex] is a positive integer.
| Quantity A | Quantity B |
| The number of units of the product that machine [latex]R[latex], working alone at its constant rate, produces in [latex]3[latex] hours | The number of units of the product that machine [latex]S[latex], working alone at its constant rate, produces in [latex]4[latex] hours |
4. In a driving competition, Jeff and Dennis drove the same course at average speeds of [latex]51[latex] miles per hour and [latex]54[latex] miles per hour, respectively. If it took Jeff [latex]40[latex] minutes to drive the course, how long did it take Dennis?
5. Working alone at its constant rate, machine [latex]A[latex] takes [latex]3[latex] hours to produce a batch of identical computer parts. Working alone at its constant rate, machine [latex]B[latex] takes [latex]2[latex] hours to produce an identical batch of parts. How long will it take the two machines, working simultaneously at their respective constant rates, to produce an identical batch of parts?
6. Two people start jogging at the same point and time but in opposite directions. If the rate of one jogger is [latex]2[latex] mph faster than the other and after [latex]3[latex] hours they are [latex]30[latex] miles apart, what is the rate of the faster jogger?
(A) [latex]3[latex]
(B) [latex]4[latex]
(C) [latex]5[latex]
(D) [latex]6[latex]
(E) [latex]7[latex]
7. A cyclist travels at [latex]12[latex] miles per hour. How many minutes will it take him to travel [latex]24[latex] miles?
(A) [latex]1[latex]
(B) [latex]2[latex]
(C) [latex]30[latex]
(D) [latex]60[latex]
(E) [latex]120[latex]
8. Train [latex]X[latex] leaves New York at [latex]10:00[latex]AM and travels East at a constant speed of [latex]x[latex] miles per hour. If another Train [latex]Y[latex] leaves New York at [latex]11:30[latex]AM and travels East along the same tracks at speed [latex]4x/3[latex], then at what time will Train [latex]Y[latex] catch Train [latex]X[latex]?
(A) [latex]2[latex] PM of the same day
(B) [latex]3[latex] PM of the same day
(C) [latex]3:30[latex] PM of the same day
(D) [latex]4[latex] PM of the same day
(E) [latex]8[latex] PM of the same day
9. An old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is [latex]36[latex] times the difference between the two numbers. How many coins did the old man have?
(A) [latex]24[latex]
(B) [latex]26[latex]
(C) [latex]30[latex]
(D) [latex]36[latex]
(E) [latex]40[latex]
10. A man walks at a rate of [latex]10[latex] mph. After every ten miles, he rests for [latex]6[latex] minutes. How much time does he take to walk [latex]50[latex] miles?
(A) [latex]300[latex]
(B) [latex]318[latex]
(C) [latex]322[latex]
(D) [latex]324[latex]
(E) [latex]330[latex]
11. Mike and Fritz ran a [latex]30[latex]-mile Marathon. Mike ran [latex]10[latex] miles at [latex]10[latex] miles per hour and then ran at [latex]5[latex] miles per hour for the remaining [latex]20[latex] miles. Fritz ran the first one-third (by time) of the run at [latex]10[latex] miles per hour and the remaining two-thirds of the run at [latex]5[latex] miles per hour. How much time in hours did Mike take to complete the Marathon?
(A) [latex]3[latex]
(B) [latex]3.5[latex]
(C) [latex]4[latex]
(D) [latex]4.5[latex]
(E) [latex]5[latex]
12. A standard machine fills paint cans at a rate of [latex]1[latex] gallon every [latex]4[latex] minutes. A deluxe machine fills gallons of paint at twice the rate of a standard machine. How many hours will it take a standard machine and a deluxe machine, working together, to fill [latex]135[latex] gallons of paint?
(A) [latex]1[latex]
(B) [latex]1.5[latex]
(C) [latex]2[latex]
(D) [latex]2.5[latex]
(E) [latex]3[latex]
13. Rajesh traveled from home to school at [latex]30[latex] miles per hour, then returned home at [latex]40[latex] miles per hour to retrieve a forgotten item, and finally returned back to school at [latex]60[latex] miles per hour, all along the same route. What was his average speed for the entire trip, in miles per hour?
(A) [latex]32[latex]
(B) [latex]36[latex]
(C) [latex]40[latex]
(D) [latex]45[latex]
(E) [latex]47[latex]
14. Lamont traveled [latex]80[latex] miles in [latex]2.5[latex] hours, at a constant rate. He then decreased his speed by [latex]25[latex]% and traveled [latex]120[latex] additional miles at the new constant rate. How many hours did the entire journey take?
(A) [latex]6.25[latex]
(B) [latex]7.5[latex]
(C) [latex]8.75[latex]
(D) [latex]10[latex]
(E) [latex]11.25[latex]
15. Machine [latex]A[latex], which produces [latex]15[latex] golf clubs per hour, fills a production lot in [latex]6[latex] hours. Machine [latex]B[latex] fills the same production lot in [latex]1.5[latex] hours. How many golf clubs does Machine [latex]B[latex] produce per hour?
Answer:
1 C
2 6 mins
3 A
4 37.8 mins
5 1 hour, 12 mins.
6 D
7 E
8 D
9 D
10 D
11 E
12 E
13 C
14 B
15 60 golf clubs per hour
