Linda and Bobby are reading copies of the same book, at different cons

Question

Linda and Bobby are reading copies of the same book, at different constant rates. Linda reads 75 pages per hour and started reading at 1:15 p.m. while Bobby reads 52 pages per hour and started reading at 12:30 p.m. What time will they be reading the same page?

A. 2:10 p.m.
B. 2:27 p.m.
C. 2:34 p.m.
D. 2:56 p.m.
E. 3:00 p.m.

A. 2:10 p.m.
B. 2:27 p.m.
C. 2:34 p.m.
D. 2:56 p.m.
E. 3:00 p.m.

GMATinsight · Answer

Linda reads 75 pages per hour

Bobby reads 52 pages per hour

i.e, Relative speed @which the gap between the read pages change = 75-52 = 23 pages per hour

Headstart of Bobby = Pages read in 15+30 i.e 45 minutes i.e. 3/4 hours (From 1:15 to 12:30) = 52*3/4 = 13*3 pages

The time to finish the gap between the two = Total Gap / Rate at which the gap changes = 39/23 = 1.7 hours = 1 hours 42 minutes

Answer: Option D

JeffTargetTestPrep · Answer

Lindas rate is 75 pages per hour and Bobby’s is 52 pages per hour. Converting 45 minutes to 3/4 hour, we can let Bobby’s time = t + 3/4 and Linda’s time = t. Let’s determine the time it will take for them to be on the same page:

52(t + 3/4) = 75t

52t + 39 = 75t

39 = 23t

39/23 = t

The answer of 39/23 hours = 39/23 x 60 ≈ 101.7 minutes. Thus, they will be on the same page 101 minutes after Linda began at 1:15 p.m. Since 101 minutes = 1 hr 41 min, thus they will be on the same page at:

1:15 p.m. + 1 hr 41 min = 2:56 p.m.

Answer: D

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Linda and Bobby are reading copies of the same book, at different cons

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