Question

Nhan and Phuong both left town A for town B at 5 am . After 5 hours , Nhan and Phuong were 102 km and 52 km away from town B respectively . The ratio of Nhan's speed to Phuong's speed was 3 : 4 and their speeds remained the same the whole journey . At what time did Nhan reach town B ? Show your full work.​

Answer 1

Nhan reach town B at 13:24 pm

Explanation:

Let

Speed of Nhan=3x km /hour

Speed of Phoung=4x km/hour

After 5 hours,

Distance covered by Nhan=3x(5)=15 xkm

Distance covered by Phuong=4x(5)=20x km

Total distance covered by Nhan to reach town B=15x+102 km

Total distance covered by Phuong to reach town B=20x+52 km

Distance between town A and town B for both person is same therefore,

`15x+102=20x+52`

`102-52=20x-15x`

`50=5x`

`x=10`

Speed of Nhan=3(10)=30 km/h

Speed of Phuong=4(10)=40 km/h

Total distance between town A and town B=102+15(10)=252 km

Time taken by Nhan to reach town B from town A=
`(distance)/(speed)`

Time taken by Nhan to reach town B from town A=
`(252)/(30)=8.4 hours`

`8.4 hours=8+0.4* 60`

=8 hours 24 minutes

1 hour=60 minutes

Nhan reach town B at 13:24 pm