You travel on the highway at a rate of $60 m p h$ for $1$ hour and at $50 m p h$ for $2$ hours and $40 m p h$ for $3$ hours. What is your average speed during the trip?

48 m p h

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47 m p h

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46 m p h

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45 m p h

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Solution

The correct option is C $47 m p h$
$\Rightarrow$ Divide the whole trip into three intervals;
$1.$ Travel at a speed of $60 m p h$ for $1 h r$ .
$2.$ Travel at a speed of $50 m p h$ for $2 h r$ .
$3.$ Travel at a speed of $40 m p h$ for $3 h r$ .
$x = v t$
$1.$ Speed is $60 m p h$ , time is $1 h r$ , then
$x_{1} = v_{1} t_{1} = 60 \times 1 = 60 m i l e s$
$2.$ Speed is $50 m p h$ , time is $2 h r$ , then
$x_{2} = v_{2} t_{2} = 50 \times 2 = 100 m i l e s$
$3.$ Speed is $40 m p h$ , time is $3 h r$ , then
$x_{3} = v_{3} t_{3} = 40 \times 3 = 120 m i l e s$
Then the total traveled distance is
$x_{t o t a l} = x_{1} + x_{2} + x_{3}$
$= 60 + 100 + 120 = 280 m i l e s$
The average speed is defined as the ratio of total traveled distance and the total traveled time. The total traveled time is
$t_{t o t a l} = t_{1} + t_{2} + t_{3} = 1 + 2 + 3 = 6 h r$
Average speed
$v_{a v} = \frac{X_{t o t a l}}{t_{t o t a l}} = \frac{280}{6} = 40 \times 3$
$= 47 m p h$

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You travel on the highway at a rate of 60mph for 1 hour and at 50mph for 2 hours and 40mph for 3 hours. What is your average speed during the trip?

You travel on the highway at a rate of $60 m p h$ for $1$ hour and at $50 m p h$ for $2$ hours and $40 m p h$ for $3$ hours. What is your average speed during the trip?