:Q 1. A plane flies 420 miles an hour. How many miles will it cover in 30 seconds? (a) 3 1/2 mi. (b) 4 mi. (c) 2 mi. (d) 3 1/4 mi. (e) 0 mi. :RCA 1. (a) 3 1/2 mi. Ans. Using direct proportions: miles seconds 420 3600 --- = ---- d 30 3600d = 12600 d = 3 1/2 miles Ans. :RA :Q 2. At 11 A.M., trains A and B each start from stations 225 miles apart and travel toward each other. Train A goes 42 miles per hour; train B, 48 miles per hour. At what time will they pass each other? (a) 2 PM (b) 1:30 PM (c) 1 PM (d) 2:30 PM (e) 12:30 PM :RCB 2. (b) 1:30 PM Ans. Let n = the number of hours each of the trains travels before passing. Since d = rt, 42n = mi covered by train A 48n = mi covered by train B Sum of the distances = 225 mi 42n + 48n = 225 90n = 225 n = 2 1/2 hrs 11 AM + 2 1/2 hr = 1:30 PM Ans. :RA :Q 3. One hour after a guest has left on a bicycle trip, the hotel sends a messenger after him in an automobile to tell him of an important call. If the man rides at 8 miles an hour and the messenger travels at 48 miles an hour, in how many minutes will the messenger overtake the guest? (a) 10 (b) 5 (c) 6 (d) 12 (e) 14 :RCD 3. (d) 12 min. Ans. Let h = hours the messenger rides Therefore: h + 1 = hours the guest rides Since each travels the same distance, d = 48h = 8(h + 1) 48h = 8h + 8 40h = 8 h = 1/5 hr. = 12 min. Ans. :RA :Q 4. At a certain time, car A is 3/4 of a mile ahead of car B. If car A is going 30 miles per hour, and car B at 45 miles per hour, in how many minutes will car B catch car A? (a) 2 (b) 3 (c) 4 (d) 5 (e) 10 :RCB 4. (b) 3 min. Ans. To overtake car A in y hours, car B travels 3/4 of a mile more than car A. 45y = 3/4 + 30y (multiply by 4) 180y = 3 + 120y 60y = 3 y = 1/20 hr. = 3 min. Ans. :RA :Q 5. Larry covered the first 40 miles of a 70-mile trip at 32 miles per hour, and the rest of the trip took only 45 minutes. Find the average rate for the whole trip. (a) 35 mph (b) 36 mph (c) 30 mph (d) 19 mph (e) 18 mph :RCA 5. (a) 35 mph Ans. total distance average rate = -------------- total time total distance = 40 + 30 = 70 mi. 40 3 total time = -- + - 32 4 1 3 = 1- + - = 2 hr 4 4 70 mi average rate = ----- = 35 mph Ans. 2 hr :ET :ET Copyright ARROW INSTRUCTIONAL SYSTEMS July 1983
