Question

You commute to work a distance of 40 miles and return on the same route at the end of the day. Your average rate on the return trip is 30 miles per hour faster than your average rate on the outgoing trip. If the round trip takes 2 hours, use a rational equation and factoring to find your average rate on the outgoing trip to work?

Answer 1

Answer:

The average rate on the outgoing trip is 30 miles per hour.

Step-by-step explanation:

Consider the provided information.

You commute to work a distance of 40 miles and return on the same route at the end of the day.

Your average rate on the return trip is 30 miles per hour faster than your average rate on the outgoing trip. If the round trip takes 2 hours.

Let the average rate on the outgoing trip is x

Average rate on the return trip = x+30

As we know $Time=\frac{Distance}{Speed}$

$\frac{40}{x}+ \frac{40}{(x+30)} = 2$

$\frac{40(x+30)+40x}{x(x+30)}= 2$

$40x+1200+40x= 2(x^2+30x)$

$80x+1200= 2x^2+60x$

$2x^2-20x-1200=0$

$x^2-10x-600=0$

$x^2-30x+20x-600=0$

$(x-30)(x+20)=0$

The value of x can't be a negative number so x=30

Hence, the average rate on the outgoing trip is 30 miles per hour.