A boy goes to school at a speed of 5 km/hr. He returns at a speed of 14 km/hr. He takes a total of 8 hours for both going to school and returning. The distance (in km) between his home and school is:
29.5
To determine the distance between the boy's home and school, we can use the concept of speed, distance, and time. Let "d" be the distance in kilometers between home and school.
Step 1: Setting up the equations for time.
The time taken to go to school is computed as:
Time = Distance / Speed = d / 5
The time taken to return is:
Time = Distance / Speed = d / 14
Step 2: Establishing the total time equation.
The total time for the trip is 8 hours. Thus, the equation to represent this is:
(d / 5) + (d / 14) = 8
Step 3: Solving the equation for d.
To eliminate the fractions, find the least common multiple of 5 and 14, which is 70.
Multiply through by 70:
70(d / 5) + 70(d / 14) = 70 * 8
This simplifies to:
14d + 5d = 560
Combine like terms:
19d = 560
Solve for d:
d = 560 / 19
Step 4: Simplifying the result.
Performing the division gives:
d = 29.4736842105...
Rounding to one decimal place, we get:
d ≈ 29.5 km
Conclusion: The distance between the boy's home and school is 29.5 km.
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