Two cyclists, A and B, travel 20 km. Cyclist A travels at 30 km/h and Cyclist B travels at 40 km/h. How much…

Question

Two cyclists, A and B, travel 20 km. Cyclist A travels at 30 km/h and Cyclist B travels at 40 km/h. How much longer does Cyclist A take than Cyclist B?

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

: Cyclists A and B

Calculate the time taken by Cyclist A.
The formula for time is distance divided by speed ( $T = \frac{D}{S}$ ).
For Cyclist A:
$T_A = \frac{20 \text{ km}}{30 \text{ km/h}} = \frac{2}{3} \text{ hours}$
Calculate the time taken by Cyclist B.
For Cyclist B:
$T_B = \frac{20 \text{ km}}{40 \text{ km/h}} = \frac{1}{2} \text{ hours}$
Calculate the difference in time in hours.
$\Delta T = T_A - T_B = \frac{2}{3} \text{ hours} - \frac{1}{2} \text{ hours}$
To subtract, find a common denominator, which is 6.
$\Delta T = \frac{2 \times 2}{3 \times 2} - \frac{1 \times 3}{2 \times 3} = \frac{4}{6} - \frac{3}{6} = \frac{1}{6} \text{ hours}$
Convert the difference in time from hours to minutes.
There are 60 minutes in 1 hour.
$\Delta T_{\text{minutes}} = \frac{1}{6} \text{ hours} \times 60 \text{ minutes/hour}$ $\Delta T_{\text{minutes}} = \frac{60}{6} \text{ minutes} = 10 \text{ minutes}$
Cyclist A took $\boxed{10 \text{ minutes}}$ more than Cyclist B.

: Capacity of a tank
Identify the dimensions of the tank.
The tank is a rectangular prism (cuboid) with:
Length ( $L$ ) = 90 cm
Width ( $W$ ) = 80 cm
Height ( $H$ ) = 50 cm
Calculate the volume of the tank in cubic centimeters.
The formula for the volume of a rectangular prism is $V = L \times W \times H$ .
$V = 90 \text{ cm} \times 80 \text{ cm} \times 50 \text{ cm}$ $V = 7200 \text{ cm}^2 \times 50 \text{ cm}$ $V = 360000 \text{ cm}^3$
Convert the volume from cubic centimeters to litres.
We know that $1 \text{ litre} = 1000 \text{ cm}^3$ .
To convert cubic centimeters to litres, divide by 1000.
$V_{\text{litres}} = \frac{360000 \text{ cm}^3}{1000 \text{ cm}^3/\text{litre}}$ $V_{\text{litres}} = 360 \text{ litres}$
The capacity of the tank is $\boxed{360 \text{ litres}}$ .

Two cyclists, A and B, travel 20 km. Cyclist A travels at 30 km/h and Cyclist B travels at 40 km/h. How much longer does Cyclist A take than Cyclist B?

Step-by-step solution

Calculate the time taken by Cyclist A.

Calculate the time taken by Cyclist B.

Calculate the difference in time in hours.

Convert the difference in time from hours to minutes.

Identify the dimensions of the tank.

Calculate the volume of the tank in cubic centimeters.

Convert the volume from cubic centimeters to litres.

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