SOLUTION: A train travels to Chicago, empty, at 70 mph. It returns loaded at 60 mph. If total travel time is 6 hours and 30 minutes, how far from Chicago is the starting point?

Click here to see ALL problems on Travel Word Problems

Question 1204384: A train travels to Chicago, empty, at 70 mph. It returns loaded at 60 mph. If total travel time is 6 hours and 30 minutes, how far from Chicago is the starting point?
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:
Answer by ikleyn(52772)   (Show Source):
You can put this solution on YOUR website!
.

Let "d" be the distance from Chicago. Moving with the speed 70 mph, the train spends hours one way. Moving with the speed 60 mph, the train spends hours another way (but the same distance). So, we write this total time two-ways travel equation + = 6.5 hours. To solve, multiply both sides by 420. You will get 6d + 7d = 6.5*420, or 13d = 2730, d = 2730/13 = 210. ANSWER. One-way distance from Chicago is 210 miles.

Solved.

-------------------

Looks as a miracle ?

- - -   It is REALLY a miracle.   It is how the " time equation " works.

Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!

Here is a method for solving problems like this that is very different from the standard algebraic method shown by the other tutor.

This method solves the problem by using the ratio of the two speeds.

The ratio of speeds is 70:60 = 7:6. Since the distance both directions is the same, the ratio of times at the two speeds is 6:7.

Dividing the total time of 6.5 hours into two parts in the ratio 6:7 gives us 3 hours and 3.5 hours. This shows that the train traveled for 3 hours at 70 mph and 3.5 hours at 60 mph.

So the distance from the starting point to Chicago is 3*70 = 210 miles, or 3.5*60 = 210 miles.

ANSWER: 210 miles

Answer by josgarithmetic(39615)   (Show Source):
You can put this solution on YOUR website!

SPEED TIME DISTANCE To Chicago 70 d From Chicago 60 d Total

Solve this for d.