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A car travels at a speed of $60\,\text{km/h}$ , while a bicycle travels at a speed of $20\,\text{km/h}$ . If they both start at the same time and travel in the same direction, how long will it take for the car to be $30\,\text{kilometers}$ ahead of the bicycle?

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Rate of travel: word problems

Full solution

Q. A car travels at a speed of

60\,\text{km/h}

, while a bicycle travels at a speed of

20\,\text{km/h}

. If they both start at the same time and travel in the same direction, how long will it take for the car to be

30\,\text{kilometers}

ahead of the bicycle?

Determine Relative Speed: First, we need to determine the relative speed between the car and the bicycle since they are traveling in the same direction.
Calculate Relative Speed: The speed of the car is $60 \, \text{km/h}$ and the speed of the bicycle is $20 \, \text{km/h}$ . To find the relative speed, we subtract the speed of the bicycle from the speed of the car. $\newline$ Relative speed = Speed of car - Speed of bicycle = $60 \, \text{km/h} - 20 \, \text{km/h} = 40 \, \text{km/h}$ .
Calculate Time: Now, we need to calculate the time it takes for the car to be $30$ kilometers ahead of the bicycle using the relative speed. $\newline$ We use the formula $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$ .
Calculate Time: Plugging in the values, we get Time = $\frac{30 \, \text{km}}{40 \, \text{km/h}}$ .
Convert Time: Performing the calculation, we get $\text{Time} = 0.75$ hours.
Convert Time: Performing the calculation, we get $\text{Time} = 0.75$ hours.To convert the time from hours to minutes, we multiply by $60$ (since there are $60$ minutes in an hour). $\newline$ $0.75 \text{ hours} \times 60 \text{ minutes/hour} = 45 \text{ minutes}.$

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