Suppose that a cyclist began a 442 mi ride across a state at

Suppose that a cyclist began a 442 mi ride across a state at the western edge of the state, at the same time that car traveling toward it leaves the eastern end of the state. If the bycicle and car met after 6.5 hr and the car traveled 37.6 mph faster than the bycicle, find the average rate of each.

Solution

Let avg rate of cyclist be x mph

Let avg rate of car be (x+ 37.6) mph

Both travelling towrds eac other so, Avg speed = x+ x + 37.6

combined distance travelled by both = 442 miles

Time taken 6.5hr

So, 6.5 = 442/(2x +37.6)

13x + 244.4 = 442

13x = 197.6

x = 15.2 mph ------> cyclist avg rate

( x + 37.6) = 52,8 mph -----> avg rate of car