Kalamazoo Word Problem Need Quick Please

Question

At 3:25 pm.,a passenger train and a freight train both left Kalamazoo,Michigan.Right now,the passenge rtrain is 61.5 miles west of Kalamazoo. The freight train is now 49.5 miles east of Kalamazoo.The passenger train averages 16 miles per hour faster than the freight train.What time is it now?

Answer 1

Let's denote the passenger train's speed as P mph and the freight train's speed as F mph. We are given that P = F + 16.

The passenger train has traveled 61.5 miles west, while the freight train has traveled 49.5 miles east. The time both trains have been traveling is the same since they left Kalamazoo at the same time.

To find the time they have been traveling, we will use the formula:

Distance = Speed × Time

Let t be the time in hours that both trains have been traveling. We can set up the following equations for each train:

For the passenger train:

61.5 = P × t

For the freight train:

49.5 = F × t

Since P = F + 16, we can substitute F + 16 for P in the passenger train equation:

61.5 = (F + 16) × t

Now, we can solve for t in the freight train equation:

t = 49.5 / F

Next, substitute this expression for t into the passenger train equation:

61.5 = (F + 16) × (49.5 / F)

To solve for F, multiply both sides by F:

61.5F = 49.5(F + 16)

Expand the right side:

61.5F = 49.5F + 49.5 × 16

Subtract 49.5F from both sides:

12F = 49.5 × 16

Now, divide both sides by 12 to get F:

F = (49.5 × 16) / 12

F ≈ 65.67 mph (approx.)

Now that we have the freight train's speed, we can find the time (t):

t = 49.5 / F

t = 49.5 / 65.67

t ≈ 0.753 hours (approx.)

To convert this time to minutes, multiply the decimal part by 60:

0.753 × 60 ≈ 45.18 minutes (approx.)

Since the trains left at 3:25 pm, the current time is approximately 3:25 pm + 45 minutes = 4:10 pm.