Question

Paul drove during a snowstorm for 40 miles. When it stopped snowing, he increased his

speed by 30 miles per hour and drove for an additional 132 miles. If Paul drove for a total
of 4 hours, which equation can be used to find his average rate of speed (x) in miles per
hour during the snowstorm?

Answer 1

Let's use the formula: distance = rate x time

During the snowstorm, Paul drove for a certain amount of time, let's call it t.

Then, his distance traveled during the snowstorm would be:

distance1 = rate1 x t

After the snow stopped, Paul increased his speed by 30 mph and drove for 4 - t hours (since he drove for a total of 4 hours and spent t hours driving in the snowstorm).

Then, his distance traveled after the snowstorm would be:

distance2 = rate2 x (4 - t)

We know that in total, Paul traveled 40 + 132 = 172 miles. So, we can set up an equation:

distance1 + distance2 = total distance

rate1 x t + rate2 x (4 - t) = 172

Now, we can solve for Paul's average rate of speed (x) during the snowstorm:

rate1 = x

rate2 = x + 30

x(t) + (x + 30)(4 - t) = 172

Simplifying:

xt + 120 - xt + 30t = 172

Combining like terms:

30t + 120 = 172

Subtracting 120 from both sides:

30t = 52

Dividing by 30:

t = 1.73 hours

Now we can substitute t back into one of the equations we derived earlier:

distance1 = x(1.73)

distance2 = (x + 30)(2.27)

We know that distance1 + distance2 = 172:

x(1.73) + (x + 30)(2.27) = 172

Expanding:

1.73x + 2.27x + 68.1 = 172

Combining like terms:

4x = 103.9

Dividing by 4:

x = 25.98 mph

Therefore, Paul's average rate of speed during the snowstorm was approximately 26 mph.