Two buses leave a station at the same time and travel in opposite directions. One bus travels 9(mi)/h faster than the other. If the two buses are 847 miles apart after 7 hours, what is the rate of each bus?

Solution

Tw o b u ses l e a v e a s t a t i o n a t t h e s am e t im e an d t r a v e l in o pp os i t e d i rec t i o n s . O n e b u s t r a v e l s 9 \frac{mi}{h} f a s t er t han t h e o t h er . I f t h e tw o b u ses a re 847 mi l es a p a r t a f t er 7 h o u rs, w ha t i s t h e r a t e o f e a c h b u s ?

first bu s^{'} s speed : 65

second bu s^{'} s speed : 56

Solution steps

Translate the problem into an equation:

x \cdot 7 + (x - 9) \cdot 7 = 847

Solve for

x, x \cdot 7 + (x - 9) \cdot 7 = 847 : x = 65

Find speed

first bu s^{'} s speed : 65

second bu s^{'} s speed : 56