a heavy freight train made a trip of 360 miles, running part of the distance at 54 miles an hour and the rest at 48 miles an hour. if the entire trip took 7 hours, find the distance traveled at each rate
For 4 hours, the train traveled at 54 miles per hour. This is:
4 x 54 = 216
For 3 hours, the rain traveled at 48 miles per hour.
3 x 48 = 144
Now, add the two totals:
144 + 216 = 360
I hope this helps?
P.S. I don't know if I didn't it right, but see if this helps.
To find the distance traveled at each rate, we can use the formula:
Distance = Speed * Time
Let's assume that the train traveled x miles at 54 miles per hour, and (360 - x) miles at 48 miles per hour.
First, let's find the time taken for each part of the trip:
Time taken at 54 mph = Distance traveled at 54 mph / Speed at 54 mph
= x / 54
Time taken at 48 mph = Distance traveled at 48 mph / Speed at 48 mph
= (360 - x) / 48
Since the total time for the trip is given as 7 hours, we can write the equation:
Time taken at 54 mph + Time taken at 48 mph = Total time
x / 54 + (360 - x) / 48 = 7
To solve this equation, we can simplify it by finding a common denominator:
(48x + 54(360 - x)) / (54 * 48) = 7
Multiplying both sides of the equation by (54 * 48) will eliminate the denominators:
48x + 54(360 - x) = 7 * (54 * 48)
Now, let's solve for x:
48x + 19440 - 54x = 7 * 2592
-6x + 19440 = 18144
-6x = 18144 - 19440
-6x = -1296
x = -1296 / -6
x = 216
Therefore, the train traveled 216 miles at 54 miles per hour and (360 - 216) = 144 miles at 48 miles per hour.