Question

A remote-controlled boat traveled 18 feet heading west and 24 feet heading south, totaling 42 feet over the course of 10 seconds. Heading west, the boat traveled at an average speed of 3 feet per seconds less than its speed heading south. What was the average speed of the boat heading west? (Do not include the units in your response.)

Answer 1

Answer:

3 ft/s

Explanation:

given,

distance in west, d₁ = 18 ft

distance in south, d₂ = 24 ft

time taken to travel 42 ft = 10 s

speed of boat in north = x ft/s

Speed of the boat when heading west = (x - 3) ft/s

$Average\ speed = \dfrac{total\ distance}{total\ time}$

$v_{avg}= \dfrac{42}{10}$

$v_{avg}= 4.2\ ft/s$

again using the above formula

now, total time

t = t₁ + t₂

$10 = \dfrac{18}{x-3} + \dfrac{24}{x}$

on simplifying

10 x² -72 x + 72 = 0

On solving the above equation we get

x = 6 ft/s

Hence, speed of boat in west direction, 6 -3 = 3 ft/s

           speed of boat in south direction = 6 ft/s