A man runs to a telephone and back in 15 minutes. His speed on the way to telephone is 15 m/s and his speed on the way back is 4m/s. Find the distance to the telephone.
let the time one way be t seconds, then the time the other way has to be 900-t seconds. (15 x 60 seconds = 900 seconds)
distance one way = 15t
distance the other way = 4(900-t)
same distance either way, so
15t = 4(900-t)
19t = 3600
t = 3600/19
distance = 15(3600/19) m or 2842.1 m or appr 2.84 km
To find the distance to the telephone, we can use the equation:
distance = speed × time
Let's assume the distance to the telephone is "d".
On the way to the telephone, the man's speed is 15 m/s, and the time taken is unknown. Let's call it "t1".
Therefore, we can write the equation:
d = 15 × t1
On the way back, the man's speed is 4 m/s, and the time taken is also unknown. Let's call it "t2".
Therefore, we can write another equation:
d = 4 × t2
We're given that the total time taken is 15 minutes, which can be converted to seconds by multiplying by 60:
15 minutes = 15 × 60 = 900 seconds
We can also write the equation for the total time:
t1 + t2 = 900
Now, we need to solve this system of equations to find the values of "t1" and "t2", and then substitute them into either equation to find the distance "d".
From the first equation, we can isolate "t1":
t1 = d / 15
Substitute this into the second equation:
d = 4 × (900 - t1)
Substitute the value of t1 from the first equation:
d = 4 × (900 - (d / 15))
Simplify the equation:
d = 3600 - (4d / 15)
Multiply the equation by 15 to eliminate the fraction:
15d = 54000 - 4d
Add 4d to both sides of the equation:
19d = 54000
Divide both sides by 19:
d = 54000 / 19
Solve for "d" using a calculator:
d ≈ 2842.11 meters
Therefore, the distance to the telephone is approximately 2842.11 meters.
To find the distance to the telephone, we need to use the formula:
Distance = Speed × Time
Let's break down the information given in the question:
- Speed on the way to the telephone: 15 m/s
- Speed on the way back: 4 m/s
- Total time for the round trip: 15 minutes
First, let's convert the time into seconds since we are using speed in meters per second:
Total time = 15 minutes × 60 seconds/minute = 900 seconds
Let's calculate the time taken to reach the telephone and the time taken to return:
Time to reach the telephone = Total time × (speed on the way to the telephone / sum of speeds)
= 900 seconds × (15 m/s / (15 m/s + 4 m/s))
= 900 seconds × (15 / 19)
= 711.58 seconds
Time to return = Total time - Time to reach the telephone
= 900 seconds - 711.58 seconds
= 188.42 seconds
Now, we can calculate the distance using the formula mentioned earlier:
Distance to the telephone = Speed on the way to the telephone × Time to reach the telephone
= 15 m/s × 711.58 seconds
= 10,673.7 meters
Therefore, the distance to the telephone is approximately 10,673.7 meters.