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Question

Brenda drove 500 miles to Las Vegas. Because of traffic, her average speed on the return trip was 20 less than her average speed going to Las Vegas. If the return trip took 2 hours longer, how fast did she drive in each direction?

Answer 1

One side distance d = 500 miles

Average speed to Las Vegas = v miles/hr.

Time to reach Las Vegas = t hours.

Formula : Distance = Speed × Time

500 = v × t

vt = 500   ⇒   t = 500/v

Average speed on the return trip was 20 less than her average speed going to Las Vegas.

Average return speed from Las Vegas = v - 20

The return trip took 2 hours longer.

Time of return from Las Vegas = t + 2 hours.

Distance = Speed × Time  ⇒  500 = ( v - 20 ) ( t + 2 )

500 = vt - 20t + 2v - 40

Substitute : vt = 500  and  t = 500/v

500 = 500 - 20(500/v) + 2v - 40

-(10000/v) + 2v - 40 = 0

-(10000 + 2v² - 40v ) / v = 0

2v² - 40v - 10000 = 0

v² - 20v - 5000 = 0

Speed cannot be negative.So - 61.4 is neglected.

So v = 81.4  miles/hr

Average return speed from Las Vegas = v - 20 = 81.4 - 20 = 61.4 miles/hr

Solution :

Average speed to Las Vegas is 81.4  miles/hr

Average return speed from Las Vegas is 61.4 miles/hr.