SOLUTION: a bus leaves at 5.00pm for a 273 mile trip to vegas.this week it left at 5:15pm.to arrive in vegas on time the driver drives 7 miles per hour faster than usual.what is the usual s

Question 722402: a bus leaves at 5.00pm for a 273 mile trip to vegas.this week it left at 5:15pm.to arrive in vegas on time the driver drives 7 miles per hour faster than usual.what is the usual speed ?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Usual speed= x
Distance = 273 miles
speed increased by 7 miles/h

It leaves 1/4 hour late reaches on time
It takes 1/4 hour less

Usual Time- time taken today = 1/4

273 /x- 273 /(x+ 7 )= 1/4

Multiply by the LCD

273 * 4 (x+ 7 )- 273 * 4 x= x(x+ 4 )
1092 (x+ 7 )- 1092 x= X^2 + 4 x
1092 x+ 7644 - 1092 x= X^2 + 4 x
x^2+ 4 x= 7644
complete the squares

(x+ 2 )^2= 7644+ 4
take the square root

x+ 2 =+/-

x+ 2 =+/- 87.45

so x = 85.45Usual speed= x
Distance = 273 miles
speed increased by 7 miles/h

It leaves 1/4 hour late reaches on time
It takes 1/4 hour less

Usual Time- time taken today = 1/4 4

273 /x- 273 /(x+ 7 )= 1/4

Multiply by the LCD

273 * 4 (x+ 7 )- 273 * 4 x= x(x+ 4 )
1092 (x+ 7 )- 1092 x= X^2 + 4 x
1092 x+ 7644 - 1092 x= X^2 + 4 x
x^2 4 x- 7644 =0
complete the squares

(x+ 2 )^2= 7644 4
take the square root

x+ 2 =+/- sqrt( 7648 )

x+ 2 =+/- 87.45

so x = 85.45 mph usual speed

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