rishabhmishra wrote:
Two boys start cycling around a circular track in opposite directions at constant speeds. if the circumference of the track is 400 meters, the faster boy cycles at 10 meters per second and the slower boy cycles at 5 meters per second, how many times would they have crossed each other after cycling for 40 minutes?
A. 15
B. 30
C. 60
D. 90
E. 120
SOURCE
EXPERTSGLOBALFind combined rate per minute. (R + R). Find time required to cross paths one time (D/R).
Finally, divide total time by time per crossing. Answer equals the # of times they meet.
Convert seconds to minutesIf time units are different, you can convert X seconds to one minute. Multiply the rate's number of seconds by N to get to 60 seconds. Multiply the numerator by N, too.
Rate of Boy 1:
\((\frac{10m}{1sec}*\frac{60}{60})=(\frac{600m}{60secs})=\frac{600m}{1min}\)Rate of Boy 2:
\((
\frac{5m}{1sec})=(\frac{300m}{60secs})=\frac{300m}{1min}\)Add ratesWhen travelers move in opposite directions, whether towards or away from one another, add rates (speeds). Combined rate:
\(\frac{600m}{1min} + \frac{300m}{1min}=\frac{900m}{1min}\)Time it takes for them to cross paths
once?
\(R*T = D\), so \(T=\frac{D}{R}\)
\(T=\frac{400m}{900\frac{meters}{minute}}=\frac{400}{900}mins=\frac{4}{9}min\) for them to meet once
Number of times they cross/meet?\(\frac{TotalMinutes}{MinutesPerOneMeet}=\) # of times they meet
\(\frac{40}{\frac{4}{9}}=40*\frac{9}{4}=90\) times that they meet
Answer D
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58% (02:01) correct 
