Math word problems

Question

A truck can travel 120 miles in the same time that it takes a car to travel 260 miles. If the trucks rate is 35 miles faster find the average rate for both

Answer 1

The problem states that the truck travels less miles at a faster speed while the car travels more miles at a slower

speed. If this is the case the times can't possibly be the same !!  You meant to say either the truck's rate is 35 mph slower or the car's rate is 35 mph faster .

Assume the truck's rate is 35 mph slower.

d=rt

120=(r-35)t for the truck

260=rt for the car

120/(r-35)=t

260/r=t

120/(r-35)=260/r

cross multiply

120r=260(r-35)

120r=260r-9100

120r-260r=-9100

-140r=-9100

140r=9100

r=9100/140=910/14=130/2=65

r=65 mph for the car

r-35=65-35=30 mph for the truck

check: 120=30t and t=120/30=4 hours

           260=65t and t=260/65=4 hours