**Answer:**

42 mph

**Step-by-step explanation:**

If you start with the assumption that the answer is an integer, you can solve a problem like this by looking at the factors of 294.

294 = 2·3·7² = 6·49 = 7·42

At 42 mph, the 294-mile trip took ...

time = distance/speed = 294 mi/(42 mi/h) = 7 h

At a speed 7 mph faster, the 294-mile trip took ...

(294 mi)/(49 mi/h) = 6 h . . . . . 1 hour less

**The average speed of Imogene's car for the 294-mile trip was 42 miles per hour**.

_____

<em>Alternative solution</em>

If you let s represent Imogene's speed, you can use the above time and distance relationship to write an equation relating the trip times:

294/s = 294/(s+7) +1

Multiplying by s(s+7), we get ...

294(s+7) = 294s +s(s+7)

2058 = s^2 +7s . . . . . . . . . . . subtract 294s

We can complete the square by adding (7/2)^2 = 12.25 to both sides

2070.25 = s^2 +7s +12.25 = (s +3.5)^2

±45.5 = s +3.5 . . . . . take the square root; next subtract 3.5

-3.5 +45.5 = s = 42 . . . . use the positive solution

**Imogene's average speed was 42 mph**.