Math Problem Statement

Harpreet covered a certain distance at 5 km/h in 4 hours 12 minutes. Find the time required to cover the same distance at the speed of 7 km/h.

Solution

To solve this problem, we can break it down into two steps:

Step 1: Calculate the distance covered by Harpreet

Given:

  • Speed = 5 km/h
  • Time = 4 hours 12 minutes

First, convert 4 hours 12 minutes into hours: 4 hours 12 minutes=4+1260=4.2 hours\text{4 hours 12 minutes} = 4 + \frac{12}{60} = 4.2 \text{ hours}

Now, use the formula: Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time} Distance=5 km/h×4.2 hours=21 km\text{Distance} = 5 \text{ km/h} \times 4.2 \text{ hours} = 21 \text{ km}

Step 2: Find the time required to cover the same distance at 7 km/h

Given:

  • Speed = 7 km/h
  • Distance = 21 km

Use the formula: Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}} Time=21 km7 km/h=3 hours\text{Time} = \frac{21 \text{ km}}{7 \text{ km/h}} = 3 \text{ hours}

So, the time required to cover the same distance at 7 km/h is 3 hours.

Would you like any further details or explanations? Here are five related questions:

  1. How would the time change if Harpreet's speed were 10 km/h?
  2. What is the formula for speed if you know the distance and time?
  3. How would you convert 4 hours 12 minutes into minutes only?
  4. What would be the distance covered if Harpreet traveled for 5 hours at 7 km/h?
  5. How does speed affect the time taken to cover a fixed distance?

Tip: Always ensure that time units are consistent when performing calculations involving speed and time.

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Math Problem Analysis

Mathematical Concepts

Speed, Distance, Time Calculations

Formulas

Distance = Speed × Time
Time = Distance / Speed

Theorems

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Suitable Grade Level

Grades 6-8