A bus leaves a station at 1p.m. traveling west at an average rate of 44 mi/h.one hour later a second bus leaves the same station traveling east at a rate of 48mi/h. At what time will the two buses be 274 miles apart

Question

A bus leaves a station at 1p.m. traveling west at an average rate of 44 mi/h.one hour later a second bus leaves the same station traveling east at a rate of 48mi/h. At what time will the two buses be 274 miles apart

I know that I am suppose to use
d=r*t

1st bus
d=44*t
2nd bus
d=48*t-1

distance is 274
so the equation for the first bus should be
274=44*t
second bus
274=48*t-1

first bus
274-44=t
230=t

second bus
274=48*t-1
274=48t-1
I believe i have missed something or messed up please explain to me what i am doing wrong please

Were is the 1 coming from?

Answer 1

v=speed x=time

The v1 for first bus is 44mi/h, v2 for second bus is 48mi/h.
We want to find the time it takes for the distance between those two buses reached 274mi.
The second bus departs after the first bus traveled for one hour. So the distance between them is 44mi.
Thus, 44+44x+48x=274mi ; 44+92x=274mi ; 92x=230mi ----> x=2.5 hours.
Answer will be 3:30 pm.

Answer 2

To solve this problem, you need to set up a system of equations to represent the distance each bus has traveled over time. Let's denote the time (in hours) that the second bus travels as "t".

The first bus leaves the station at 1 p.m., so it has already been traveling for one hour when the second bus starts. Therefore, the time for the first bus can be represented as (t + 1) since it has been traveling for one more hour than the second bus.

Now, let's set up the equations for the distances traveled by each bus:

Distance traveled by the first bus: d1 = 44 * (t + 1)
Distance traveled by the second bus: d2 = 48 * t

Since the two buses are moving in opposite directions, the total distance between them is the sum of their distances:

d1 + d2 = 274

Substituting the expressions for d1 and d2 into the equation:

44 * (t + 1) + 48 * t = 274

Now, simplify the equation:

44t + 44 + 48t = 274
92t + 44 = 274

To isolate the variable t, subtract 44 from both sides of the equation:

92t = 230

Divide both sides by 92:

t = 2.5

Therefore, the second bus has been traveling for 2.5 hours.

To find the time at which the two buses will be 274 miles apart, we add the travel time of the second bus to the starting time of 1 p.m.:

1 p.m. + 2.5 hours = 3:30 p.m.

So, the two buses will be 274 miles apart at 3:30 p.m.