Question

A bus traveled at an average rate of 50 miles per hour and then reduced its average rate to 40 miles per hour for the rest of the trip. If the 200-mile trip took 5 hour, determine how long the bus traveled at each rate.

Answer 1

@50 mph
let distance = x
time1= distance/rate = x/50

@40mph
distance=220-x
time2 = distance/rate =(220-x)/40

time1+time2 = 5
x/50 + (220-x)/40 = 5
solve for x
x=100

at 50mph
distance = 100 miles

at 40mph
distance = 220-100 = 120 miles

Answer 2

5 hours @ 40 mph, zero hours @ 50 mph.

lalaly's equation from above is:
\[\frac{x}{50}+\frac{220-x}{40}\text{=}5 \]The problem with this equation is that the trip distance, as stated in the problem, is 200 miles, not 220 miles.

Solve the following for x:\[\frac{x}{50}+\frac{200-x}{40}\text{=}5\]x = 0
No distance was traveled @ 50mph and all 5 hours were traveled @ 40mph.
40mph * 5 hours = 200 miles

Answer 3

The solution to\[\frac{x}{40}+\frac{200-x}{50}\text{=}5\]is x = 200
Again, the bus traveled 200-200 or zero miles @ 50 mph and 200/40 = 5 hours @ 40 mph.

Answer 4

my bad...sorry