A word problem wanting the speed

Question

On her road bike, Cassie bikes 15 km/hr faster than Demy on her mountain bike. In the time it takes Cassie to travel 80 km, Demy travels 50 km. Find the speed of each bicyclist.

Answer 1

distance = rate x time

 

80 = (r+15)*t ---> 80/(r+15) = t

 

50 = r*t ---> 50/r = t

 

80/(r+15) = 50/r <--- times are the same, as stated in the problem

 

80r = 50(r+15) <--- cross multiplies

 

80r = 50r + 750

 

30r = 750

 

r = 25

 

Demy speed is 25 km/hr

Cassie speed is 40 km/hr

 

Demy travels 50 km in 2 hours

Cassie travels 80 km in 2 hours