Algebra word question

Question

Suppose that a cyclist began a 420 mi ride across a state at the western edge of the state, at the same time that a far traveling toward it leaves the eastern end of the state. If the bicycle and car met after 7.5 hr and the car traveled 30.4 mph faster than the bicycle, find the average rate of each

Answer 1

d_c + d_b = 420                         sum of distances

7.5(r +30.4) + 7.5(r) = 420    d = r · t

7.5r + 228 + 7.5r = 420         distribute

15r + 228 = 420                     combine like terms

15r = 192                                subtract 228 from both sides

r = 12.8

 

The bicycle traveled at 12.8 mph. The car traveled at 43.2 mph.