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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!

Answer

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

 

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Thanks for your help

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