Problem Solving

The two important things to recognize are that:
1. The travel times will be equal when they meet.
2. A will have traveled 4.5 laps and B will therefore have traveled 3.5 laps because that is the first time they have met.

cheers.

Alphonsaj wrote:"A" and "B" run around a circular track starting from the same point simultaneously in the same direction. "A" meets "B" for the first time when "A" is exactly in the middle of his 5th round. If "A" is faster than "B" and take 70 seconds to complete 1 lap, how long will B take to complete 1 lap?

A) 90 seconds
B) 54.44 seconds
C) 110 seconds
D) 63 seconds
E) 77 seconds

Since A and B meet for the first time when A has traveled 4.5 laps at a rate of 70 seconds per lap, the time required for A and B to meet = (4.5)(70) = 315 seconds.
We can PLUG IN THE ANSWERS, which represent B's time per lap.
Since A is faster than B, B's time per lap must be GREATER than A's time per lap.
Eliminate B and D.
When the correct answer choice is plugged in, B will be exactly halfway around the track after traveling for 315 seconds.

E: 77 seconds
At a rate of 77 seconds per lap, the number of laps traveled by B in 315 seconds = 315/77 = 45/11 laps.
Since B is not exactly halfway around the track, eliminate E.

A: 90 seconds
At a rate of 90 seconds per lap, the number of laps traveled by B in 315 seconds = 315/90 = 35/10 = 3.5 laps.
Success!

The correct answer is A.

Alphonsaj wrote:I'm sorry.
But I don't get, how we arrived at 3.5 laps.

Once A has caught back up to B, it will have completed exactly one more lap than B has completed. If A is halfway through its fifth lap, it will have completed 4.5 laps. Because we know this is exactly one more lap than B will have completed, B will have completed 3.5 laps at this point.

Alphonsaj wrote:I'm sorry.
But I don't get, how we arrived at 3.5 laps.

For A to meet B again, he must have run ONE LAP MORE than B: they're at the same place on the track, but A is moving faster, so he must have passed that place once more than B has. (A can't have run more than one lap more than B, or he would've already passed him.)

From there, we discover that A travels 4.5 laps in the time it takes B to travel 3.5 laps, or at a rate (4.5/3.5) => 9/7 of B's rate. Since A takes 70 seconds to complete a lap, B must take (9/7) of that, or (9/7) * 70 => 90 seconds.