A Difficult Word Problem

Question

At the same time two trains leave chicago and new york they move towards each other at constant speeds the train from chicago is going 40 mph and the train from new york is going 60 mph the distanc e between chicago and new york is 1000 miles how long after there departure will they meet

Answer 1

Let x = time it takes for the trains to meet

 

Distance = (Rate)(Time)

 

Distance traveled by first train in x hours = 40x miles

Distance traveled by second train in x hours = 60x miles

 

When the trains meet, the total distance traveled by the two trains is 1000 miles.

 

So, 40x + 60x = 1000

 

               100x = 1000

 

                    x = 10 hours

Answer 2

Hello there!

 

When we have 2 objects moving towards each other , then the effective or the combined speed is added.

So when the trains move in a constant speed , the effective speed will be (40+60) = 100 mph

 

Now, distance between the 2 places is 1000 miles.

 

We can use the formula , time = Distance / Speed and say time taken = 1000/100 = 10 Hrs

 

OR

 

We can say that the 2 trains combined cover 100 miles in 1 hr. So they cover 1000 miles in 10 hours.

 

Hence the answer is 10Hr.

 

Always check - for the first train - in 10 hours it will cover 400 miles . and the second train from Newyork will cover 600 miles. (sum of the distance is 1000 miles)