Problem Solving

Jerry and Ross decide to have a footrace. They run 1,000 meters. Jerry runs 5 meters per second and Ross 4 meters per second. Halfway through the race, Jerry realizes he is ahead and stops running for one full minute before finishing the race at the same speed. Who wins the race?

A. Jerry
B. Ross
C. Both

The OA is B.

I need to determine the total time that each one takes to complete the 1,000 meters, then
$$T_{Jerry}=\frac{1000}{5}+60=260$$
and
$$T_{Ross}=\frac{1000}{4}=250$$
That's mean Ross wins the race, right?

Experts, any suggestion about this PS question? Thanks in advance.

LUANDATO wrote:Jerry and Ross decide to have a footrace. They run 1,000 meters. Jerry runs 5 meters per second and Ross 4 meters per second. Halfway through the race, Jerry realizes he is ahead and stops running for one full minute before finishing the race at the same speed. Who wins the race?

A. Jerry
B. Ross
C. Both

The OA is B.

I need to determine the total time that each one takes to complete the 1,000 meters, then
$$T_{Jerry}=\frac{1000}{5}+60=260$$
and
$$T_{Ross}=\frac{1000}{4}=250$$
That's mean Ross wins the race, right?

Experts, any suggestion about this PS question? Thanks in advance.

Hello LUANDATO.

Your answer is great and very fast. Another way you can do it (but is a bit longer than yours) is the following:

Jerry ran at 5 mts/sec during 500 meters, then they ran during $$t=\frac{500}{5}=100\ \text{seconds}$$

On the other hand, in 100 secs Ross ran $$d=4\cdot100=400\ mts$$

At this point, the distance between them is 100 meters. Now, Jerry stopped for 1 minute=60 seconds. During this time Ross continued running and he advanced: $$d=4\cdot60=240\ mts$$ At this moment, Jerry has run 500 meters and Ross 400+240=640 meters.

Now, the race starts again. The question is: who arrives first? To answer this, we calculate the time need for each one arrives to the finish.

Jerry left 500 meters, hence his time will be $$t=\frac{500}{5}=100\ \text{seconds}$$ and Ross left 360 meters, hence his time is $$t=\frac{360}{4}=90\ \text{seconds}$$ This implies that Ross won the race.

I hope this answer also can help you.

I'm available f you'd like a follow-up.