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.

Question

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Respuesta :

lublana lublana · Answer 1 · 2021-06-15T06:29:35+02:00

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,

[tex]15x+102=20x+52[/tex]

[tex]102-52=20x-15x[/tex]

[tex]50=5x[/tex]

[tex]x=10[/tex]

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=[tex]\frac{distance}{speed}[/tex]

Time taken by Nhan to reach town B from town A=[tex]\frac{252}{30}=8.4 hours[/tex]

[tex]8.4 hours=8+0.4\times 60[/tex]

=8 hours 24 minutes

1 hour=60 minutes

Nhan reach town B at 13:24 pm