Passenger train leaves 2 hours after a freight train leaves. The freight train travels 14 mph slower than the passenger train. Find the rate of each train if the passenger train overtakes the freight train in 3 hours.
I did this :
5r=3(r+14)
5=3r+28
2r=28
Freight train =14 mph
Passenger = 28 mph
Can you please correct me I'm not quite sure how to do this problem
so as I read it, five hours after the freight train leaves.
so the distance the passenger train travels is 3*VP=3((Vt+14)
distance the freight train travels is
5(Vt) But the distances are equal
5Vt=3Vt+42
vt=21 mph
vp=35
so recheck your math, especially what is 3 times 14
The freight travels r mi/h.
The passenger train travels r+14 mi/h.
Df = Dp.
5r = 3(r+14)
5r = 3r + 42
r = 21 mi/h.
r+14 = 21 + 14 = 35 mi/h.
Laura, Your Eq is correct, but you made an error when solving it.
Thank you for your feedback!
I have realized my mistakes
To solve this problem correctly, let's break it down step by step:
1. Let's denote the rate (speed) of the passenger train as "p" mph.
2. Since the freight train is traveling 14 mph slower, its rate will be "p - 14" mph.
3. The time it takes for the passenger train to overtake the freight train is 3 hours.
Now, let's set up the equation to solve for the rate of each train:
Distance traveled by the freight train = Distance traveled by the passenger train
Since distance = rate × time, we can write:
(p - 14) × 3 = p × 5
Let's solve this equation:
3p - 42 = 5p
2p = 42
p = 21
The rate of the passenger train is 21 mph.
To find the rate of the freight train, substitute this value back into the equation:
(p - 14) = 21 - 14 = 7
The rate of the freight train is 7 mph.
Therefore, the passenger train travels at 21 mph, and the freight train travels at 7 mph.