Tom runs empty-handed from one side of a yard to the other side at a

Question

Tom runs empty-handed from one side of a yard to the other side at a constant speed. He returns at half the speed holding a heavy ball. It takes him 5 seconds longer to run with the ball than empty-handed. If the yard is 60 meters long, how many seconds did it take Tom to run across the yard while holding the ball?

A. 4
B. 5
C. 6
D. 8
E. 10

A. 4
B. 5
C. 6
D. 8
E. 10

sumitkrocks · Answer

Speed with which Tom runs without ball = x
Speed with ball in hands = x/2 
xt=60 
x/2* (t+5) = 60 
Solving for x and t we get 
x= 12 t=5 
Time taken by tom with ball in hand to cross the fence = 5+5 =10 sec

KarishmaB · Answer

Since his speed is 1/2 on return, time taken will be 2 times. Since he takes 5 sec extra on return, he must be taking 5 secs when empty handed and 10 sec on return.

Answer (E)

MathRevolution · Answer

Yard = 60 metres = Distance

Let speed (empty hand) be = 12 mps

Time taken =  \frac{60 }{12} = 5 sec

Return speed (heavy ball) =  \frac{12}{2} = 6 mps

Time taken =  \frac{60 }{ 6} = 10 sec.

Answer E

pierjoejoe · Answer

DST164

for this kind of problems i like to use a technique i saw a couple of times on the forum.

in this case the distance is the same, so we equate times:

	distance	speed	time
without heavy ball	60	v	60/v
with heavy ball	60	v/2	60/v/2 = 120/v

now we know that when he is faster he takes 5 less seconds, meaning that the higher time (when he is slower), minus the lower time (when he is faster) = 5
in this case:

120/v-60/v = 5

solving for v --> v = 12

we know time = 120/v with the ball --> time = 120/12 = 10

i find it so much easier and less confusing. in general i like to convert every mutation of this problem in such a way that is solvable with this strategy. i made a little collection of similar problem to practice it!

https://gmatclub.com/forum/in-a-100-met ... 80581.html
https://gmatclub.com/forum/harvey-runs- ... 99049.html
https://gmatclub.com/forum/a-trip-of-90 ... 54768.html
https://gmatclub.com/forum/today-dave-d ... 95328.html
https://gmatclub.com/forum/if-a-man-wal ... 14111.html
https://gmatclub.com/forum/alex-and-ben ... 33915.html
https://gmatclub.com/forum/a-and-b-star ... 19329.html
https://gmatclub.com/forum/tom-runs-emp ... 56140.html

Tom runs empty-handed from one side of a yard to the other side at a

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Tom runs empty-handed from one side of a yard to the other side at a

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards