how do you set up this equation?

Question

A bus travels 60mph, a car travels at 40mph. how long will it take a bus to pass car if car has a 1.5hr lead?

How exactly do you go about setting up the equation..I have trouble with word problems and would like to have the work showed to me step by step. thanks

Answer 1

Figure out what you know.

Distance = rate*time/D = rt

Rate of bus = 60 mph
Rate of car = 40 mph

Time bus has been going = we don't know, so "x"
Time car has been going = we don't know, but we know it's 1.5 hours longer than the bus has, since the car got a head start, so "x+1.5"

So now we've figured out both rate and time for the bus and the car. What about distance?

Well, we want to know how long it will take for the bus to pass the car. When the bus passes the car, how far are they both going to be from the starting point? We don't know, but they have to be at the same place--that is, the same distance.

So what this question is asking us to find is how long it will take for the distance traveled by the bus and the distance traveled by the car to be the SAME, or Dcar = Dbus, so rt (car) = rt (bus).

Now we have all the information we need. Plug in the values into the equation, and you should get:
40(x + 1.5) = 60(x)

Solve for x and you've got your answer.

Answer 2

Use the speed formula
v=speed
d=distance
t=time
v=d/t
first thing we have to understand that we have 2 values for the car the speed and the time which will figure out what the distance is
so for the car v=40, t=1.5, d=?
for the bus v=60, t=?, d=?

Then if the bus reaches the car it means they travelled the same distance therefore,

d= vt = distance for car= distance for bus
d= 40 x 1.5 = 60 x t
= 56=60t
:. t = 56/60
t = 0.9333333 ...... hrs
therefore it takes the bus 0.93 hrs to pass the car.

DOes this explain it???
just remember if the bus needs to pass the car that means they are at the same distance which means distance is equal for both car and bus ... you have the time for the car which is 1.5h the only missing part is time for bus to get the distance.

Answer 3

60x distance traveled by bus

40x+60 distance traveled by car

where x is the time traveled (in hours)

set the 2 equations equal to one another.

60x=40x+60
20x=60
x=3

after 3 hours