# A car travels 140 km in 3.5 hours and a train travels 30 km in 50 min. What is the ratio of the speed of the car to that of the train?

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1
Feb 7, 2018

The ratio is $10 : 9$.

#### Explanation:

Divide $\text{140 km}$ by $3.5$ hours to get the $\text{km/hour}$.

$\frac{140}{3.5} = 40$

The car travels at $\text{40 km/hour}$.

For the train, you have to make the conversion to per hour.

$\text{30 km in 50 min = 3 km in 5 min = 36 km in 60 min}$

Therefore, The train travels at $\text{36 km/hour}$.

So

$\text{Car " : " Train} = 40 : 36$

This is the ratio, which can be simplified to $10 : 9$.

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Feb 7, 2018

$10 : 9$

#### Explanation:

Car: $\frac{140}{3.5} = 40$

Train: $\frac{30}{50} = \frac{x}{60} \implies 50 x = 1800 \implies x = 36$

Ratio: $40 : 36$ = $10 : 9$

Yay!

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Feb 7, 2018

70:63

#### Explanation:

To find the ratio, you have to get a common base. First, convert 3.5 hours into minutes to get a common base (210 min).simplify to get a simplified ratio.

14 km : 21 min (car, divide each by 10)

3 km : 5 min (train, divide each by 10)

The LCM of the times (21 and 5, since you want to find the ratio of the speed of the car to the speed of the train) is 105.

Multiply 14 and 21 by 5, and you get the ratio

70 km : 105 min (car)

Multiply 3 and 5 by 21, and you get the ratio

63 km : 105 min (train).

Now that you have common bases, you can find the car speed to the train speed.

70:105
63:105, so

70:63

**Edit: you can simplify this to 10:9

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