college algebra word problem

Question

if a car travels 280 miles averaging a certain speed. if the car had gone 5 mph faster, the trip would have taken 1 hour less. What was the average speed?

Answer 1

S = speed (mi/hr)

T = trip time (hr)

 

Distance = S*T = 280 miles

 

From the 2nd sentence:

( S + 5 )( T - 1 ) = 280

 

rewrite the 1st equation

T = 280/S

 

substitute into the 2nd equation

( S + 5 )( 280/S - 1 ) = 280

 

expand and simplify

280 - S + 5*280/S - 5 = 280

-S + 1400/S - 5 = 0

 

 

Multiply by S:

- S^2 - 5S + 1400 = 0

 

S^2 + 5S - 1400 = 0

 

Can we factor this?  Look at the factors of 1400: 2, 2, 2, 5, 5, 7---40, 35  (Yes--difference it 5)

 

So:

( S + 40 )( S -35 ) = 0

The only useful solution is S = 35

then T = 280/35 = 8

 

CHECK:

( S+5 )( T-1 ) = 280

 

40 * 7 = 280 OK!!!

Answer 2

Hi Angela,

 

let x = mph

let t = hrs

 

280 = speed * time

 

280 = x*t

 

but if the car goes 5 mph faster it travels in 1 less hour

 

so

 

280 = (x+5)*(t-1)

 

280 = xt + 5t -x -5

 

280 = 280 + 5t -x -5

 

0 = 5t -x -5

 

x = 5t - 5

 

replace in first equation

 

280 = (5t-5) * t

 

280 = 5t² - 5t

 

0 = 5t² - 5t - 280

 

now factor

 

0 = (5t - 40)(t+7)

 

solve for the value of t that is positive

 

0 = 5t -40

 

5t = 40

 

t = 8

 

280 = 8x

 

x = 35           average speed  for 8 hours

 

Hope this helps