Tom drove to Easton from home at 50 mph. His return trip took 30 minutes longer because he ran into traffic and could only drive 45mph. How many miles is it from Tom's home to Easton? Express answer as a decimal.
D = RT (Distance = Rate x Time)
50 = rate going
T = time going
50T = distance going
45 = rate returning
T + .5 = time returning (30/60 = .5h)
45(T + .5) = distance returning
Distances are equal
50T = 45(T + .5)
50T = 45T + 22.5
5T = 22.5
T = 4.5 h
50T = distance going
50(4.5) = 225 miles
Answer as a decimal?
Thank you so much, helper!
m
Well, it seems like Tom really got caught up in a tight spot! Let's calculate the distance from his home to Easton, shall we?
If we assume the distance from his home to Easton is "x" miles, then the time it took him to drive at 50 mph would be x/50 hours.
On the return trip, he drove at 45 mph, which took 30 minutes longer. Now, 30 minutes is equal to 0.5 hours. So, the time it took on the return trip would be (x/45) + 0.5 hours.
Since we know these two times are equal, we can set up an equation:
x/50 = (x/45) + 0.5
Now, let's solve it.
Multiply everything by 450, so we get rid of those pesky denominators:
9x = 10x + 225
Now, let's isolate x by subtracting 10x from both sides:
-1x = 225
Wait, where did x go?
Oh well, it looks like x has run off to join a circus!
So the answer is...
x = 225 miles!
Tom's distance from home to Easton is 225 miles. Hopefully, he doesn't run into too much traffic next time!
To find the distance from Tom's home to Easton, we will use the formula: distance = speed × time.
Let's assume that the distance from Tom's home to Easton is represented by 'd' miles.
First, we'll calculate the time it took Tom to drive to Easton. Since he was driving at 50 mph, we can write the equation as:
time = distance / speed = d / 50 hours
Next, we'll calculate the time it took Tom for the return trip. Since he could only drive 45 mph, we can write the equation as:
time (return trip) = distance / speed = d / 45 hours
According to the problem, the return trip took 30 minutes (or 0.5 hours) longer than the trip to Easton. So we can set up the equation:
time (return trip) = time (trip to Easton) + 0.5
Substituting the values we calculated earlier, we get:
d / 45 = d / 50 + 0.5
To solve this equation, we can start by eliminating the denominators by multiplying all terms by the least common multiple (LCM) of 45 and 50, which is 450:
450 * (d / 45) = 450 * (d / 50) + 450 * 0.5
After simplification, we have:
10d = 9d + 225
Now, let's isolate the variable 'd' by subtracting 9d from both sides:
10d - 9d = 225
Simplifying further, we get:
d = 225
Therefore, the distance from Tom's home to Easton is 225 miles.