how do I solve this and show the work:
a motorboat went upstream at 15 miles per hour and returned downstream at 20 miles per hour. How far did the boat travel one way if the round trip took 3.5 hours?
since time = distance/speed, add up the total time:
d/15 + d/20 = 3.5
d = 30
To solve this problem, we can use the formula:
Time = Distance / Speed
Let's assume that the distance traveled one way is D miles.
The time taken to go upstream is D / 15 hours, and the time taken to go downstream is D / 20 hours.
Given that the round trip took 3.5 hours, we can set up the equation:
D / 15 + D / 20 = 3.5
To solve this equation, we can find a common denominator and simplify. The common denominator here is 60.
Multiply the equation by 60 to get rid of the denominators:
4D + 3D = 210
Combine like terms:
7D = 210
Divide both sides of the equation by 7:
D = 30
Therefore, the boat traveled a distance of 30 miles one way.
To solve this problem, you can use the formula:
Distance = Speed * Time
Let's break down the problem step by step:
1. Let's assume the distance between the starting and ending points is 'd' miles.
2. Given that the boat went upstream at 15 miles per hour, we can calculate the time it took for the upstream journey. Using the formula Time = Distance / Speed, we have:
Time upstream = d / 15
3. Similarly, since the boat returned downstream at 20 miles per hour, we can calculate the time for the downstream journey:
Time downstream = d / 20
4. We know that the total round trip took 3.5 hours. Therefore, the total time taken for both the upstream and downstream journeys can be expressed as:
Total time = Time upstream + Time downstream
Substituting the values, we have:
3.5 = d / 15 + d / 20
5. To solve for 'd', we can start by finding a common denominator for the fractions on the right-hand side. Multiplying each term by 60 (common denominator of 15 and 20), we have:
210 = 4d + 3d
Simplifying, we get:
210 = 7d
6. Divide both sides by 7 to solve for 'd':
d = 210 / 7
d = 30
Therefore, the distance the boat traveled one way is 30 miles.