Yosief and his family went to San Diego for summer vacation. Yosief plotted the speed versus time on his note book see below. Estimate the distance to San Diego using Yosief's plot?

Apr 20, 2016

Approximately $340$ miles

Explanation:

From A to B
$\textcolor{w h i t e}{\text{XXX}}$time $= \frac{1}{2}$ hr.
$\textcolor{w h i t e}{\text{XXX}}$ave. speed $= \frac{0 + 38}{2}$ mph $= 19$ mph
$\textcolor{w h i t e}{\text{XXX}}$distance $= \frac{1}{2}$ hr $\times 19$ mph $= 9 \frac{1}{2}$ miles.

From B to C
$\textcolor{w h i t e}{\text{XXX}}$time $= \frac{1}{2}$ hr.
$\textcolor{w h i t e}{\text{XXX}}$ave. speed $= \frac{38 + 40}{2}$ mph $= 39$ mph
$\textcolor{w h i t e}{\text{XXX}}$distance $= \frac{1}{2}$ hr $\times 39$ mph $= 19 \frac{1}{2}$ miles.

From C to D
$\textcolor{w h i t e}{\text{XXX}}$time $= \frac{1}{4}$ hr.
$\textcolor{w h i t e}{\text{XXX}}$ave. speed $= \frac{40 + 70}{2}$ mph $= 55$ mph
$\textcolor{w h i t e}{\text{XXX}}$distance $= \frac{1}{4}$ hr $\times 55$ mph $= 13 \frac{3}{4}$ miles.

From D to E
$\textcolor{w h i t e}{\text{XXX}}$time $= 3 \frac{3}{4}$ hr. $= \frac{15}{4}$ hr.
$\textcolor{w h i t e}{\text{XXX}}$ave. speed $= \frac{70 + 70}{2}$ mph $= 70$ mph
$\textcolor{w h i t e}{\text{XXX}}$distance $= \frac{15}{4}$ hr $\times 70$ mph $= 262 \frac{1}{2}$ miles.

From E to F
$\textcolor{w h i t e}{\text{XXX}}$time $= 1$ hr.
$\textcolor{w h i t e}{\text{XXX}}$ave. speed $= \frac{70 + 0}{2}$ mph $= 35$ mph
$\textcolor{w h i t e}{\text{XXX}}$distance $= 1$ hr $\times 35$ mph $= 35$ miles.

Total Distance to San Diego
$\textcolor{w h i t e}{\text{XXX}} 9 \frac{1}{2} + 19 \frac{1}{2} + 13 \frac{3}{4} + 262 \frac{1}{2} + 35$ miles
$\textcolor{w h i t e}{\text{XXX}} = 340 \frac{1}{4}$ miles