Question

A moving van leaves a house traveling at an average rate of 40 mi/h. The family leaves the house 1/2 hour later following the same route in a car. They travel at an average rate of 60 mi/h.

Write an expression for the time traveled by the car. Then solve.

Answer 1

lets call the time the moving van left the house t. speed is 40mi/hr. the family leaves 30 minutes later, aka, t+30, where t is measured in minutes. speed is 60mi/hr.
thats how far i can go. are you sure you copied the question correctly? "write an equation for the time traveled by the car" ? is it time or distance?

Answer 2

the time

Answer 3

i dont think you understand what I'm trying to talk about. You cant just say "write an equation for the time traveled by the car". you cannot "travel" time. You can, however, cover a distance. So was the question something like "what time did they meet" ? or how long did it take both vehicles to travel blah blah miles?

Answer 4

Anyway, i'll assume you meant when they meet each other. so here we go:
we know distance = speed*time
distance(truck) = speed(truck) * time(truck)
distance(car) = speed(car) * time(car)
Rearranging this for the time of the car (your question ? ) gives t(car)=speed(car)/distance(car)
we also know that the time of the car is 30 minutes less than the trucks car. so we can say t(truck) = t(car) + 0.5 (btw, i used 0.5 because the question said miles per HOUR, so, make all your time units into hours not minute. this means 30 minutes is 0.5 hours. you with me so far? )

Answer 5

anyway, lets recount all the equations we have now:
1. distance(truck) = speed(truck) * time(truck)
2. distance(car) = speed(car) * time(car)
3. t(car)=speed(car)/distance(car)
4. t(truck)=speed(truck)/distance(truck)
5. t(truck) = t(car) + 0.5

If you rearrange 5, you get: t(truck) - 0.5 = t(car). we'll call this (6)
But from number 4, we know that t(truck) is speed of truck/distance traveled by truck. so substituting 4 into 6, we get:
[speed(truck)/ distance (truck) ] -0.5 = t(car)

now if im correct, thats the equation you're looking for.

Answer 6

going ahead, if you want to find when the car overtakes the truck, we know their distance would have to be the same. speed of truck is 40m/hr. speed of car is 60 m/hr.

solve for when the distances of the car is 0 and the truck are the same (because the car is faster than the truck, its not ALWAYS going to be 30 minutes behind the truck. in fact, it could actually get to their new house QUICKER if it was far enough LOL)

d=s/t
d(truck) = d(car)
speed(truck)/time (truck) = speed(car)/time (car)
but remember time (car) is time(truck) plus 0.5
so we have speed(truck)/time (truck) = speed(car)/[time (truck)+0.5]
solve for everything, and you'd find out that they are both at the same place when the time of the truck is one hour.

but remember the car is 30 mins behind? so if you I in the car, I'd go past the truck in 90 minutes and if you were in the truck, you'd see me waving hi to you after one hour.

Answer 7

Hope i could answer your question. Anyway, its already one week, so im pretty sure im late LOL