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

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)

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• Alvin
Lv 4
2 years ago

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

• 2 years ago

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.