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# Two boys start cycling around a circular track in opposite directions

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Manager
Joined: 23 Sep 2016
Posts: 230
Two boys start cycling around a circular track in opposite directions [#permalink]

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08 Mar 2018, 04:17
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Difficulty:

55% (hard)

Question Stats:

51% (01:37) correct 49% (01:47) wrong based on 79 sessions

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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

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Manager
Joined: 23 Sep 2016
Posts: 230
Re: Two boys start cycling around a circular track in opposite directions [#permalink]

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08 Mar 2018, 04:26
1
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 EXPERTSGLOBAL

SOLU lets first find out when they both will meet
as we all know both cyclist are coming towards each other they will meet soon so total distance must be divided by sum of their speed.
total distance will be 400 meters circumference of circle
so 400/10+5= 400/15
=80/3 in every 80/3 seconds they will meet
so in 40 min they will meet
40*60(convert in seconds)
we will divide total time with they took time to meet once so to identify how many times they met.
40*60*3/80
=90
so OA IS D
VP
Joined: 07 Dec 2014
Posts: 1020
Two boys start cycling around a circular track in opposite directions [#permalink]

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08 Mar 2018, 12:25
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 EXPERTSGLOBAL

400m/15 combined mps=26 2/3 seconds until first crossing
40 min*60 sec=2400 seconds
2400/(26 2/3)=90 crossings
D
SC Moderator
Joined: 22 May 2016
Posts: 1763
Two boys start cycling around a circular track in opposite directions [#permalink]

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11 Mar 2018, 16:09
1
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 EXPERTSGLOBAL

Find 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 minutes

If 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:
$$( \frac{5m}{1sec})=(\frac{300m}{60secs})=\frac{300m}{1min}$$

When 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

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Re: Two boys start cycling around a circular track in opposite directions [#permalink]

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12 Mar 2018, 10:08
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

We can let t = the time they will meet for the first time:

10t + 5t = 400

15t = 400

t = 400/15 = 80/3 seconds

Since 40 minutes = 40 x 60 = 2,400 seconds, they will meet 2,400/(80/3) = (2,400 x 3)/80 = 30 x 3 = 90 times.

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Re: Two boys start cycling around a circular track in opposite directions   [#permalink] 12 Mar 2018, 10:08
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