Problem 1Cities and are miles apart. Alicia lives in and Beth lives in . Alicia bikes towards at 18 miles per hour. Leaving at the same time, Beth bikes toward at 12 miles per hour. How many miles from City will they be when they meet?
Question
Problem 1Cities and are miles apart. Alicia lives in and Beth lives in . Alicia bikes towards at 18 miles per hour. Leaving at the same time, Beth bikes toward at 12 miles per hour. How many miles from City will they be when they meet?
Solution
Step 1: Determine the combined speed of Alicia and Beth.
Alicia is biking at 18 miles per hour and Beth is biking at 12 miles per hour. When they bike towards each other, their speeds add up. So, their combined speed is 18 mph + 12 mph = 30 mph.
Step 2: Determine the time it takes for Alicia and Beth to meet.
Since they start at the same time and bike towards each other, they will meet somewhere in between the two cities. The time it takes for them to meet is the total distance between the two cities divided by their combined speed.
However, the problem does not provide the distance between the two cities. Let's assume the distance between the two cities is D miles. Then, the time it takes for them to meet is D miles / 30 mph.
Step 3: Determine the distance Alicia travels before they meet.
The distance Alicia travels is her speed times the time it takes for them to meet. So, the distance Alicia travels is 18 mph * (D miles / 30 mph) = 0.6D miles.
So, when Alicia and Beth meet, they will be 0.6D miles from City A.
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