A trucks varying distance from the warehouse d measured in m

A truck\'s varying distance from the warehouse, d, measured in miles is modeled by the formula d = t^2 + 50t where t is the varying number of hours since the truck left the warehouse. The truck\'s destination is 422 miles away. How many hours will it take the truck to reach its destination? _ hours A car left the warehouse at the same time as the truck and wants to get to the destination at the same time. What constant speed would the car have to travel in order to reach the destination at the same time as the truck? miles per hour

Solution

Solution:

since distance is modelled with function d = t^2 +50t

let at time t when it reached to the destination then it would have travelled distance d = 422 miles

plug d =422 in modelled function

422 = t^2 +50t

on solving this equation we get

t= 1047 -25 and t=-25-1047

we ignore -ve value of time t

t= 1047 -25 hours

truck reach at its desitination

answer

(b)
since total distance = 422 miles

and time taken by truck to cover this distance t= 1047 -25

therefore average speed of truck will be the constant speed of so that both can reach at same time

constant speed of car = 422/(1047 -25) = 25 + 1047 = 57.35 miles per hour

annswer