Henry drives 150 miles at 30 miles per hour and then another 200 miles at 50 miles per hour. What was his average speed, in miles per hour, for the entire journey, to the nearest hundredth?

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38.89

48.00

42.33

34.58

answer is A.

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Detailed Solution

We know the distance covered d by an object is the length of shortest possible path from the initial position to the latter position. If we measure the time from point of start as t then the speed v is the distance covered per unit time. It is given by the formula
v =

\frac{s}{t}

t =

\frac{s}{v}

Let us denote the distance covered by Henry in the initially as d1=150 and the speed as v1=30 miles/hour. So the time taken t1 by Henry to cover the first 30 miles in hours is
t1 =

\frac{d_{1}}{v_{1}}

\frac{150}{30}

= 50
Similarly the distance covered by Henry, after the increase in speed as d2 and the speed as v2=50 miles/hour. So we have d2 = 200 and v2 = 50 miles/hour. So the time taken t1 by Henry to cover the latter 50 miles in hours is
t1 =

\frac{d_{2}}{v_{2}}

= 40
The total time taken t by Henry to travel the entire journey is the sum of time taken for first 30 miles and then latter 50 miles which means
t = t1 + t2 = 50 hours + 40 hours = 90 hours The total distance travelled by Henry d in miles is
d = d1 + d2 = 150 + 200 = 450 miles So the average speed v of Henry to cover the entire journey is total distance travelled divided by total time taken that is,
v =

\frac{d}{t}

\frac{350}{9}

= 38.8888...
We are asked to find the speed to the nearest hundred. So we round off up to two digits after the decimal and conclude that the speed was 38.89 miles per hour.
So, the correct answer is “Option 1”.

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