Question

A truck driver travels three-fourths the distance of his run at 20 mph and then completes his run at 10 mph. What was the trucker's average speed for the trip?

Answer 1

Given:

A truck driver travels three-fourths the distance of his run at 20 mph and then completes his run at 10 mph.

To find:

Trucker's average speed.

Calculation:

Average speed is often defined as the total distance divided by the total time taken to cover that specified distance.

Let total distance be s:

$\therefore \: avg. \: v = \dfrac{total \: distance}{total \: time}$

$= > \: avg. \: v = \dfrac{s}{ \bigg( \dfrac{ \frac{3s}{4} }{20} \bigg) + \bigg( \dfrac{ \frac{s}{4} }{10} \bigg) }$

Cancelling "s" from both numerator and denominator:

$= > \: avg. \: v = \dfrac{1}{ \bigg( \dfrac{ \frac{3}{4} }{20} \bigg) + \bigg( \dfrac{ \frac{1}{4} }{10} \bigg) }$

$= > \: avg. \: v = \dfrac{1}{ \bigg( \dfrac{ 3 }{80} \bigg) + \bigg( \dfrac{ 1}{40} \bigg) }$

$= > \: avg. \: v = \dfrac{1}{ \bigg( \dfrac{ 3 + 2 }{80} \bigg) }$

$= > \: avg. \: v = \dfrac{1}{ \bigg( \dfrac{5}{80} \bigg) }$

$= > \: avg. \: v = \dfrac{80}{5 }$

$= > \: avg. \: v = 16 \: mph$

So, final answer is:

$\boxed{ \bold{ \large{\: avg. \: v = 16 \: mph}}}$