Can you help to solve this elementary school (Singapore) math problem?

Question

At 7 a.m., Ben and his sister left their house and cycled to school. Ben cycled at a speed of 4km/h faster than his sister. When Ben reached his school, he realised he had left his wallet at home and he immediately cycled back home to get his wallet. After cycling 400m from school, he met his sister on the way. What time did Ben meet his sister on his way back? (Source: Nanyang)

Alvin · Accepted Answer

sister travelled  sist_dist =   distance to school -  400 m   
ben travelled  distance to school + 400 m

d = rt   
have Both ben and his sister travelled the same time 
sister's rate (speed) =  s 
 ben's speed =s + 4

distance to school -  400 =  t(s) 
convert to distance to km's 
Sister's equation
distance to school - 0.4 km = t(s)
Ben's equation  
distance to school + 0.4 km  = t(s+4)  = ts + 4t

subtract 2nd equation from 1st

-0.8  meters =  -4 (km/h)t 
-0.8 km  = -4 (km/h ) t 
t = 0.8/ 4 =  0.2 hours or   1/5 of an hours = 60 * 1/5 = 12 minutes

so if you started 7:00 AM then, they meet at 7:12 AM

ideaquest · Answer

But remember this is an elementary school problem.
If we see the problem as a relative speed,

Then relative speed of 4 km/h would cover 0.4 x 2 km.

So, time taken is 0.8 / 4 = 0.2 hour = 12 minutes.

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Can you help to solve this elementary school (Singapore) math problem?

2 Answers