Question

Two​ vehicles, a car and a​ truck, leave an intersection at the same time. The car heads east at an average speed of 20 miles per​ hour, while the truck heads south at an average speed of 50 miles per hour. Find an expression for their distance apart d​ (in miles) at the end of t hours.

Answer 1

Answer:

$d = 10\times t\sqrt{29}miles$

Explanation:

Given:

't' hour be the time taken for travel by  both the vehicles and 'd'  be the distance between then

then

Distance traveled by the car = 20 × t miles

and

Distance traveled by the truck  = 50 × t miles

now, using the Pythagoras theorem

$d = \sqrt{(20t)^2+(50t)^2}$

or

$d = \sqrt{400t^2+2500t^2}$

or

$d = \sqrt{2900t^2}$

or

$d = 10\times t\sqrt{29}$

thus, the equation relating the distance 'd' with the time 't' comes as

$d = 10\times t\sqrt{29}miles$