Asked by Rachel h

A teacher drove 280 miles to attend a mathematics conference and arrived 1 hour late. The teacher figured out that, had she increased her average speed by 5 mph, she would have arrived on time to the conference. What was her average rate of speed?

*explanations would be awesome if possible because i have a test on this tomorrow and have NO clue how to do it..thanks!
Answered by drwls

Let T be the time of the trip in hours, if one arrives on time. Let V be the speed he first time.
280/V = T+1
280/(V+5)= T

Solve the two equations for the two unknowns.

1/V - 1 = 1/(V+5)

1(V+5)/V - (V+5) = 1
1 + 5/V - V -5 = 1

-V^2 -5V + 5 = 0
Take the positive root of the quadratic equation.

Check my thinking
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