Question

two trains are 333 miles apart, and their speeds differ by 13 mph. find the speed of each train if they are traveling toward each other and will meet in 3 hours. mph (smaller value) mph (larger value)

Explanation:

Step1: Define variables

Let the speed of the slower train be \( x \) mph. Then the speed of the faster train is \( x + 13 \) mph.

Step2: Calculate relative speed and distance

Since they are moving towards each other, their relative speed is the sum of their speeds, which is \( x+(x + 13)=2x + 13 \) mph. They meet in 3 hours and the total distance between them is 333 miles. We know that distance \( d=\text{speed}\times\text{time} \), so \( 3(2x + 13)=333 \).

Step3: Solve the equation

First, divide both sides of the equation by 3: \( 2x+13=\frac{333}{3}=111 \). Then subtract 13 from both sides: \( 2x=111 - 13 = 98 \). Then divide both sides by 2: \( x=\frac{98}{2}=49 \).

Step4: Find the speeds

The speed of the slower train is \( x = 49 \) mph. The speed of the faster train is \( x + 13=49+13 = 62 \) mph.

Answer:

Smaller value: 49 mph, Larger value: 62 mph