Jim paddles from one shore of a lake three miles wide at 4 mph, and John paddles from the opposite
shore at 5 mph. How long will they travel before they meet?
please explain to me
let Jim's distance be x miles
then John's distance is 3-x miles
Jim's time = x/4
John's time = (3-x)/5
when they meet, they will both have paddled the same time
so ...
x/4 = (3-x)/5
5x = 12 - 4x
9x = 12
x = 12/9 miles
so Jim's time = (12/9) /4 = 1/3 hour or 20 minutes
or, you can consider it like this. The boats are approaching each other at 9 mph. The lake is 3 miles wide, so it takes them 1/3 hour to cover all the distance.
To find the time it takes for Jim and John to meet, we can use the formula:
Time = Distance / Speed
Let's assume that when they meet, they have both traveled a total distance of x miles.
Jim travels at 4 mph, so in time t, he covers a distance of 4t miles.
Similarly, John travels at 5 mph, so in time t, he covers a distance of 5t miles.
Since the total distance is x miles, we can set up the equation:
4t + 5t = x
Combining like terms, we get:
9t = x
Since the width of the lake is 3 miles, when they meet, they will have covered a total distance of 3 miles.
Substituting this into the equation, we have:
9t = 3
Simplifying further, we get:
t = 3/9
Reducing the fraction, we have:
t = 1/3
Therefore, they will travel for 1/3 of an hour or approximately 20 minutes before they meet.
To determine how long Jim and John will travel before they meet, we need to find out at what time they will be at the same position.
First, let's calculate the time it takes for Jim to paddle across the lake.
Distance = Speed * Time
Distance = 3 miles
Speed = 4 mph
Time taken by Jim = Distance / Speed = 3 miles / 4 mph = 0.75 hours.
Now let's calculate the time it takes for John to paddle across the lake.
Distance = Speed * Time
Distance = 3 miles
Speed = 5 mph
Time taken by John = Distance / Speed = 3 miles / 5 mph = 0.6 hours.
Since both Jim and John are paddling towards each other, we can add their times to find the total time they will travel before they meet.
Total Time = Time taken by Jim + Time taken by John = 0.75 hours + 0.6 hours = 1.35 hours.
Therefore, Jim and John will travel for 1.35 hours before they meet.