Math Problem Statement

(a) A car travels 100 miles at a speed of 40mph. (b) A lorry travels 90 miles at a speed of 60 mph. (c) A bus drives at a speed of 48mph and covers a distance of 60 miles. (d) A helicopter flies 105 kilometres at a speed of 140 km/h (e) A bird covers a distance of 95 miles at a speed of 20 miles per hour: (f) A car travels at 50 mph and covers a distance of 110 miles. (g) A lorry drives a distance of 452.4 kilometres at a speed of 52 km/h. (h) A bird flies 80 miles at a speed of 15 miles per hour (i) A ship sails 208 miles a speed of 24 miles per hour (i) A jet flies at a speed of 480km/h and covers a distance of 2088 kilometres (k) A racing car drives 256 miles at a speed of 120 mph (i) A helicopter flies 764 kilometres at a speed of 80 km/h

Solution

To solve this set of questions, we need to calculate the time it takes for each vehicle, bird, or object to travel a given distance at a given speed. The formula for time is:

Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}

I will now calculate the time taken for each part:

(a) Car:

  • Distance = 100 miles
  • Speed = 40 mph Time=100 miles40 mph=2.5 hours\text{Time} = \frac{100 \text{ miles}}{40 \text{ mph}} = 2.5 \text{ hours}

(b) Lorry:

  • Distance = 90 miles
  • Speed = 60 mph Time=90 miles60 mph=1.5 hours\text{Time} = \frac{90 \text{ miles}}{60 \text{ mph}} = 1.5 \text{ hours}

(c) Bus:

  • Distance = 60 miles
  • Speed = 48 mph Time=60 miles48 mph=1.25 hours\text{Time} = \frac{60 \text{ miles}}{48 \text{ mph}} = 1.25 \text{ hours}

(d) Helicopter:

  • Distance = 105 km
  • Speed = 140 km/h Time=105 km140 km/h=0.75 hours\text{Time} = \frac{105 \text{ km}}{140 \text{ km/h}} = 0.75 \text{ hours}

(e) Bird:

  • Distance = 95 miles
  • Speed = 20 mph Time=95 miles20 mph=4.75 hours\text{Time} = \frac{95 \text{ miles}}{20 \text{ mph}} = 4.75 \text{ hours}

(f) Car:

  • Distance = 110 miles
  • Speed = 50 mph Time=110 miles50 mph=2.2 hours\text{Time} = \frac{110 \text{ miles}}{50 \text{ mph}} = 2.2 \text{ hours}

(g) Lorry:

  • Distance = 452.4 km
  • Speed = 52 km/h Time=452.4 km52 km/h8.7 hours\text{Time} = \frac{452.4 \text{ km}}{52 \text{ km/h}} \approx 8.7 \text{ hours}

(h) Bird:

  • Distance = 80 miles
  • Speed = 15 mph Time=80 miles15 mph5.33 hours\text{Time} = \frac{80 \text{ miles}}{15 \text{ mph}} \approx 5.33 \text{ hours}

(i) Ship:

  • Distance = 208 miles
  • Speed = 24 mph Time=208 miles24 mph8.67 hours\text{Time} = \frac{208 \text{ miles}}{24 \text{ mph}} \approx 8.67 \text{ hours}

(j) Jet:

  • Distance = 2088 km
  • Speed = 480 km/h Time=2088 km480 km/h=4.35 hours\text{Time} = \frac{2088 \text{ km}}{480 \text{ km/h}} = 4.35 \text{ hours}

(k) Racing Car:

  • Distance = 256 miles
  • Speed = 120 mph Time=256 miles120 mph2.13 hours\text{Time} = \frac{256 \text{ miles}}{120 \text{ mph}} \approx 2.13 \text{ hours}

(l) Helicopter:

  • Distance = 764 km
  • Speed = 80 km/h Time=764 km80 km/h9.55 hours\text{Time} = \frac{764 \text{ km}}{80 \text{ km/h}} \approx 9.55 \text{ hours}

Summary of Time Taken:

  1. Car (a): 2.5 hours
  2. Lorry (b): 1.5 hours
  3. Bus (c): 1.25 hours
  4. Helicopter (d): 0.75 hours
  5. Bird (e): 4.75 hours
  6. Car (f): 2.2 hours
  7. Lorry (g): 8.7 hours
  8. Bird (h): 5.33 hours
  9. Ship (i): 8.67 hours
  10. Jet (j): 4.35 hours
  11. Racing Car (k): 2.13 hours
  12. Helicopter (l): 9.55 hours

Would you like more details on any part of the calculations? Here are some related questions:

  1. What happens if the speeds of the vehicles change?
  2. How would different units (e.g., kilometers per hour vs miles per hour) affect the calculations?
  3. How would you calculate the average speed if all vehicles traveled the same total distance?
  4. How does fuel consumption relate to speed and time of travel?
  5. What impact do varying weather conditions have on time of travel?

Tip: Always ensure that the units for distance and speed match when calculating time, or convert them appropriately before applying the formula.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Ratios
Unit Conversion
Time-Distance-Speed Relation

Formulas

Time = Distance / Speed

Theorems

-

Suitable Grade Level

Grades 6-8