# Question

Town X is 180km away from Town Z. A bus started travelling from Town X at 11.30am and travelled towards Town Z. Half an hour later, a car started from Town X, travelling at an average speed of 75km/h along the same route. The car overtook the bus and reached Town Z before the bus. The bus reached Town Z at 2.30 pm.

(a) At what time did the car overtake the bus?

(b) How far away was the bus from Town Z when the car reached Town Z?

Thanks!

(a)

Town X ———————-———- 180 km —————-———– Town Y
11.30 am, bus ——-> …………………………………………………………………..…………..…………. 2.30 pm
12 pm, car ——-> 75 km/h

11.30 am ——- 3 h ——- 2.30 pm
180/3 = 60 (speed of bus)
60 (t + 1/2) = 75t
t = 2
12pm ——- 2h ——- 2 pm

(b)
180/75 = 2.4
12 pm ——- 2.4 h ——- 2.24 pm
2 h 24 min + 30 min = 2.9 h
60 x 2.9 = 174
180 – 174 = 6

Ans : (a) 2 pm; (b) 6 km.

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First determine speed of bus. Bus left X at 11.30am and reached at 2.30 pm. Hence, it takes 3 hours to cover 180km.

Speed of bus = 60km/h

Bus had headstart of half an hour -> distance covered by car to overtake bus = 60km/h * 1/2h = 30km

The car covers this distance at 30 / 75 = 0.4 h = 24mins so

(a) car overtakes bus at 12.24pm.

At 75km/h, car reached town Z in 180/75 = 2.4h

2.4h from 12pm (half an hour after bus) is 2.24pm

The bus was 6 minutes from Town Z so

(b) distance of bus from Town Z = 0.1h * 60km/h = 6km

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This is a DST question.

 Time Speed Distance Bus 1 0.5 60 30 Bus 2 1u 60 60u Car 1u 75 75u

14h 30min – 11h 30 min = 3 h

180 ÷ 3 = 60

30 + 60u = 75u

30 = 75u – 60u

15u = 30

1u = 30 ÷ 15 = 2

a)

11 h 30 min + 30 min + 2hr = 14 hr

They meet at 2pm

b)

75 × 2 = 150

180 – 150 = 30

30 ÷ 75 = 0.4 h

60 × 0.4 = 24 km

150 + 24 = 174

180 – 174 = 6 km