Ken and Kara are 27 miles apart on a caml lake paddling toward each other. Ken paddles at 4mph, while kara paddles at 7 mph. How long will it take them to meet?
let Ken paddle x miles, then
Kara paddles 27-x miles
time for Ken = x/4
time for Kara = (27-x)/7
When they meet, each would have paddles the same time, so
solve
x/4 = (27-x)/7
To find out how long it will take Ken and Kara to meet, we need to calculate the time it takes for them to cover the distance between them.
Let's assume that t represents the time it takes for them to meet.
Ken's speed is 4 mph, so in t hours, he will cover a distance of 4t miles.
Similarly, Kara's speed is 7 mph, so in t hours, she will cover a distance of 7t miles.
Since they are paddling towards each other, the sum of the distances they cover should be equal to the total distance between them, which is 27 miles.
So, we have the equation:
4t + 7t = 27
Combining like terms:
11t = 27
Now, divide both sides by 11:
t = 27 / 11
Calculating this, t ≈ 2.45 hours.
Therefore, it will take Ken and Kara approximately 2.45 hours (or 2 hours and 27 minutes) to meet each other.
To find out how long it will take Ken and Kara to meet, we need to calculate the time it takes for them to cover the total distance between them.
First, let's determine how far Ken and Kara each paddle in one hour:
- Ken paddles at 4 mph, so in one hour, he covers a distance of 4 miles.
- Kara paddles at 7 mph, so in one hour, she covers a distance of 7 miles.
Since they both start 27 miles apart and are paddling toward each other, the total distance they need to cover is 27 miles.
To find out how long it takes to cover this distance, we can add the distances Ken and Kara cover together and divide it by their combined speeds:
- Ken covers 4 miles in one hour.
- Kara covers 7 miles in one hour.
So together, they cover 4 + 7 = 11 miles in one hour.
Now, we can calculate the time it takes for them to meet by dividing the total distance they need to cover (27 miles) by the distance they travel together in one hour (11 miles):
27 miles / 11 miles/hour = 2.45 hours.
Therefore, it will take Ken and Kara approximately 2.45 hours, or 2 hours and 27 minutes, to meet each other.