Question

. Egbert is in a rowboat four miles from the nearest point on Egbert a straight shoreline. He wishes to reach a house 12 miles farther down the shore. If Egbert can row at a rate of 3 mi/hr and walk at a rate of 4 mi/hr, find the least amount of time required to reach the house. How far from the house should he land the rowboat? Justify your answer.

Answer 1

Answer:

$t=\frac{13}{3} =4.33\ mi.hr^{-1}$

Explanation:

Given:

• Distance from the shore, $s=4\ mi$

• distance of house from the shore, $h=12\ mi$

• speed of rowing, $v_r=3\ mi.hr^{-1}$

• speed of walking, $v_w=4\ mi.hr^{-1}$

For the least amount of time to reach the house one must row at the nearest point on the shore and then walk from there.

Now the time taken to reach the shore:

$t_s=\frac{s}{v_s}$

$t_s=\frac{4}{3}\ mi.hr^{-1}$

Time taken in walking to house from the shore:

$t_h=\frac{h}{v_w}$

$t_h=\frac{12}{4}$

$t_h=\frac{12}{4}$

$t_h=3\ mi.hr^{-1}$

Therefore total time taken:

$t=t_h+t_s$

$t=\frac{13}{3} =4.33\ mi.hr^{-1}$