# Question

At 7 am, 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.

a. What time did Ben meet his sister on his way back?

b. What was the distance from Ben’s house to the school?

(a)
house ———————————– ? km ————————————- school
7 am, Ben and sister ——->

sister’s speed : 1u
distance sister travelled : 1p
Ben’s speed : 1u + 4
distance Ben travelled : 1p + (0.4 x 2) = 1p + 0.8

1p/1u = (1p + 8)/(1u + 4)
1up + 4p = 1up + 0.8u
1p = 0.2u
1u/1p = 1/0.2 = 5 (sister’s speed)
5 + 4 = 9 (Ben’s speed)
4 km : 1 h
0.8 km : 0.2 h
7 am ————– 0.2 h —————- 7.12 am

(b)
5 x 0.2 = 1
1 + 0.4 = 1.4 (one of the many possible answers)

Ans : (a) 7.12 am; (b) 1.4 km.

For b) Should it be 1-0.4 = 0.6km? Instead of 1+0.4?

thanks

In 12 min, sister travelled 1 km (based on an assumed speed of 5 km/h) and Ben travelled 1.8 km (based on assumed speed of 9 km/h). The latter implied that Ben travelled 400 m more to reach the school and 400 m back to meet his sister.

Hence, 1 + 0.4 = 1.4. (As the speed is not well defined, there are indeed many possible answers depending on their speeds as long as the difference between the two is 4 km/h.)

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a) Ben actually opened a gap of 800m with a relative speed of 4 km/h
Time taken is 0.8/4 = 0.2 hr => 12mins

Time met = 7:12 am

Personally I think this is a flawed question for B), as the absolute speed is not defined in the question.

Any distance is possible and able to produce a gap of 800m in 12 mins.

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