A passenger train's speed is 60 mi/h, and a freight train's speed is 40 mi/h. The passenger train travels the same distance in 1.5 h less time than the freight train. How long does each train take to make the trip?
Let D=distance
Time for passenger = D/60
Time for freight = D/40
"The passenger train travels the same distance in 1.5 h less time than the freight train. "
D/40 - D/60 = 1.5
Can you complete the rest?
Jehej
To solve this problem, we can use the formula Distance = Speed * Time. Let's assume the distance traveled by both the passenger train and the freight train is represented by "D".
Let's first establish the equation for the passenger train:
Distance = Speed * Time
D = 60 * T1
Now let's establish the equation for the freight train:
Distance = Speed * Time
D = 40 * T2
Given that the passenger train travels the same distance in 1.5 hours less time than the freight train, we can write an equation:
T1 = T2 - 1.5
Now we can substitute the values of D from the second and third equations into the first equation to form an equation with T1 and T2 only:
60 * T1 = 40 * T2
Next, substitute the value of T1 from the third equation into the equation above:
60 * (T2 - 1.5) = 40 * T2
Now let's solve for T2:
60 * T2 - 90 = 40 * T2
20 * T2 = 90
T2 = 4.5
Now, substitute the value of T2 into the equation from the third equation to find T1:
T1 = T2 - 1.5
T1 = 4.5 - 1.5
T1 = 3
So, it takes the passenger train 3 hours to make the trip, and it takes the freight train 4.5 hours to make the same trip.