Sam goes to school from his house at a speed of 5 kmph and returns at a speed of 4 kmph. If he takes 9 hours in going and coming , what the distance between his house and school?
Question
Sam goes to school from his house at a speed of 5 kmph and returns at a speed of 4 kmph. If he takes 9 hours in going and coming , what the distance between his house and school?
Solution
Let's denote the distance between Sam's house and his school as D (in km).
Step 1: Calculate the time taken to go to school The time taken to go to school can be calculated using the formula Time = Distance/Speed. So, the time taken to go to school is D/5 hours.
Step 2: Calculate the time taken to return from school Similarly, the time taken to return from school is D/4 hours.
Step 3: Set up the equation According to the problem, the total time taken for going and coming is 9 hours. So, we can set up the equation as follows: D/5 + D/4 = 9
Step 4: Solve the equation To solve the equation, we first make the denominators the same. The least common multiple of 5 and 4 is 20. So, we multiply the first term by 4 and the second term by 5 to get: 4D/20 + 5D/20 = 9 This simplifies to: 9D/20 = 9 To solve for D, we multiply both sides of the equation by 20/9 to get: D = 9 * 20 / 9 This simplifies to: D = 20 km
So, the distance between Sam's house and his school is 20 km.
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