Question

Two buses leave a station at the same time and travel in opposite directions. One bus travels 16 km/h slower than the other. If the two buses are 848 km apart after 4 hours, what is the rate of each bus?

Answer 1

Speed of one bus is
`114 (km)/(h)` and speed of another bus is
`98 (km)/(h)`

Step-by-step explanation:

Let the speeds of two buses be
`v_1\, and\, v_2` respectively

Since speed of one bus is 16 km/h slower than the other

Therefore
`v_1= v_2+16(km)/(h)`

Since buses are traveling in opposite directions so relative speed of buses

`v_(rel)=v_1+v_2= v_2+16(km)/(h)+v_2=2v_2+16(km)/(h)`

Distance traveled ,
`d=v_(rel)t`

=>
`848=4(2v_2+16)`

=>
`v_2=98 (km)/(h)`

`\therefore v_1=v_2+16(km)/(h)=(98+16) (km)/(h)=114 (km)/(h)`

=>
`v_1=114 (km)/(h)`

Thus speed of one bus is
`114 (km)/(h)` and speed of another bus is
`98 (km)/(h)`