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

Answer:

Nhan reach town B at 13:24 pm

Step-by-step 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=$\frac{distance}{speed}$

Time taken by Nhan to reach town B from town A=$\frac{252}{30}=8.4 hours$

$8.4 hours=8+0.4\times 60$

=8 hours 24 minutes

1 hour=60 minutes

Nhan reach town B at 13:24 pm