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

Answer:

Speed of one bus is $114 \frac{km}{h}$  and speed of another bus is $98 \frac{km}{h}$

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 $v_1= v_2+16\frac{km}{h}$

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

$v_{rel}=v_1+v_2= v_2+16\frac{km}{h}+v_2=2v_2+16\frac{km}{h}$

Distance traveled , $d=v_{rel}t$

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

=>$v_2=98 \frac{km}{h}$

$\therefore v_1=v_2+16\frac{km}{h}=(98+16) \frac{km}{h}=114 \frac{km}{h}$

=>$v_1=114 \frac{km}{h}$

Thus speed of one bus is $114 \frac{km}{h}$  and speed of another bus is $98 \frac{km}{h}$