Distance-Time Problem: Calculate Car Travel from 200km in 4 Hours to 7 Hours

Speed-Distance Calculations with Constant Motion

A car travels a distance of 200 km in 4 hours.
What distance will it travel in 7 hours?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

A car travels a distance of 200 km in 4 hours.
What distance will it travel in 7 hours?

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the speed of the car using the formula.
  • Step 2: Calculate the distance for 7 hours using the speed.

Now, let's work through each step:
Step 1: Calculate the speed of the car. The speed is calculated by the formula:

Speed=DistanceTime=200 km4 hours=50 km/h \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{200 \text{ km}}{4 \text{ hours}} = 50 \text{ km/h}

Step 2: Use the speed to find the distance traveled in 7 hours. The distance is given by:

Distance=Speed×Time=50 km/h×7 hours=350 km \text{Distance} = \text{Speed} \times \text{Time} = 50 \text{ km/h} \times 7 \text{ hours} = 350 \text{ km}

Therefore, the car will cover a distance of 350 km in 7 hours.

3

Final Answer

350

Key Points to Remember

Essential concepts to master this topic
  • Formula: Speed equals distance divided by time for constant motion
  • Technique: Calculate speed first: 200 km ÷ 4 hours = 50 km/h
  • Check: Verify by working backwards: 50 km/h × 7 hours = 350 km ✓

Common Mistakes

Avoid these frequent errors
  • Adding hours instead of using proportional reasoning
    Don't just add 3 more hours to 200 km = 203 km! This ignores that distance depends on speed multiplied by time. Always find the speed first, then multiply by the new time period.

Practice Quiz

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What is the ratio between the orange and gray parts in the drawing?

FAQ

Everything you need to know about this question

Why can't I just add the extra 3 hours to 200 km?

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Distance isn't additive like that! You need to think about rate of travel. The car covers a certain distance per hour, so more hours means proportionally more distance covered.

What if the car doesn't travel at constant speed?

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This problem assumes constant speed (uniform motion). In real life, cars speed up and slow down, but math problems usually assume steady speed unless stated otherwise.

How do I remember the distance formula?

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Think D = S × T (Distance = Speed × Time). You can rearrange this:

  • Speed = Distance ÷ Time
  • Time = Distance ÷ Speed

Can I set up a proportion instead?

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Yes! You can write: 200 km4 hours=x km7 hours \frac{200 \text{ km}}{4 \text{ hours}} = \frac{x \text{ km}}{7 \text{ hours}} . Cross-multiply to get the same answer: 350 km.

What units should my final answer have?

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Always include units in your answer! Since the question asks for distance, your answer should be in kilometers (km), just like the given information.

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