Man and Dog

Algebra Level 3

A \rm A and B \rm B are 5 k m \rm 5\ km apart, and a man goes from A \rm A to B \rm B at a speed of 3.14 m / s \rm3.14\ m/s . Meanwhile, a dog goes from A \rm A to B \rm B at a speed of 9.87 m / s \rm9.87\ m/s . After reaching B \rm B , the dog moves back and forth between B \rm B and the man at the same speed until man reaches B \rm B .

How many meters has the dog traveled by the time the man reaches B \rm B ? Keep the answer to two decimal places.


The answer is 15716.56.

Zhiqian Chen by Zhiqian Chen , 15, China

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1 solution

Zhiqian Chen
Aug 27, 2020

Considering that dog and man start moving at the same time and stop at the same time, so

T i m e d o g = T i m e m a n = D i s t a n c e m a n V e l o c i t y m a n = 5 k m 3.14 m / s = 5000 3.14 s \rm {Time}_{dog}={Time}_{man}=\dfrac{ {Distance}_{man}}{{Velocity}_{man}}=\dfrac{5\ km}{3.14\ m/s}=\dfrac{5000}{3.14}\ s

So, we can get

D i s t a n c e d o g = V e l o c i t y d o g T i m e d o g = 9.87 m / s × 5000 3.14 s ≈ 15716.56 m \rm {Distance}_{dog}={Velocity}_{dog}{Time}_{dog}=9.87\ m/s\times\dfrac{5000}{3.14}\ s\approx\boxed{15716.56\rm\ m}

5 Helpful 1 Interesting 5 Brilliant 1 Confused

bruh shouldnt this be considered easy and not medium

gaoyi zhu - 7 months, 2 weeks ago

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