Math / Algebra

Question4 Хоёр машины нэг нь нөгөөгөөс 20\%-оор их хурдтай бол машинуудын хурдны харьцааг олоорой. Хэрэв нэг машин нь 60 км/ц хурдтай бол нөгөө машин ямар хурдтай байх вэ?

Studdy Solution

STEP 1

1. One car is 20% faster than the other car.
2. We need to find the ratio of their speeds.
3. One car's speed is given as 60 km/h.
4. We need to find the speed of the other car.

STEP 2

1. Define variables for the speeds of the two cars.
2. Express the relationship between the speeds using the given percentage.
3. Calculate the speed of the second car.
4. Determine the ratio of their speeds.

STEP 3

Define variables for the speeds of the two cars. Let $v_1$ be the speed of the slower car and $v_2$ be the speed of the faster car.

STEP 4

Express the relationship between the speeds using the given percentage. Since one car is 20% faster, we have:
$v_2 = v_1 + 0.2v_1$ $v_2 = 1.2v_1$

STEP 5

Calculate the speed of the second car. Given that $v_1 = 60$ km/h, substitute into the equation:
$v_2 = 1.2 \times 60$ $v_2 = 72 \text{ km/h}$

STEP 6

Determine the ratio of their speeds. The ratio of the speeds $v_1 : v_2$ is:
$\frac{v_1}{v_2} = \frac{60}{72}$
Simplify the ratio:
$\frac{60}{72} = \frac{5}{6}$
Thus, the ratio of their speeds is $\boxed{\frac{5}{6}}$ .

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Question4 Хоёр машины нэг нь нөгөөгөөс 20\%-оор их хурдтай бол машинуудын хурдны харьцааг олоорой. Хэрэв нэг машин нь 60 км/ц хурдтай бол нөгөө машин ямар хурдтай байх вэ?

Studdy Solution

STEP 1

1. One car is 20% faster than the other car.
2. We need to find the ratio of their speeds.
3. One car's speed is given as 60 km/h.
4. We need to find the speed of the other car.

STEP 2

1. Define variables for the speeds of the two cars.
2. Express the relationship between the speeds using the given percentage.
3. Calculate the speed of the second car.
4. Determine the ratio of their speeds.

STEP 3

Define variables for the speeds of the two cars. Let $v_1$ be the speed of the slower car and $v_2$ be the speed of the faster car.

STEP 4

Express the relationship between the speeds using the given percentage. Since one car is 20% faster, we have:
$v_2 = v_1 + 0.2v_1$ $v_2 = 1.2v_1$

STEP 5

Calculate the speed of the second car. Given that $v_1 = 60$ km/h, substitute into the equation:
$v_2 = 1.2 \times 60$ $v_2 = 72 \text{ km/h}$

STEP 6

Determine the ratio of their speeds. The ratio of the speeds $v_1 : v_2$ is:
$\frac{v_1}{v_2} = \frac{60}{72}$
Simplify the ratio:
$\frac{60}{72} = \frac{5}{6}$
Thus, the ratio of their speeds is $\boxed{\frac{5}{6}}$ .

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Question4 Хоёр машины нэг нь нөгөөгөөс 20\%-оор их хурдтай бол машинуудын хурдны харьцааг олоорой. Хэрэв нэг машин нь 60 км/ц хурдтай бол нөгөө машин ямар хурдтай байх вэ?

Studdy Solution

STEP 1

1. One car is 20% faster than the other car.2. We need to find the ratio of their speeds.3. One car's speed is given as 60 km/h.4. We need to find the speed of the other car.

STEP 2

1. Define variables for the speeds of the two cars.2. Express the relationship between the speeds using the given percentage.3. Calculate the speed of the second car.4. Determine the ratio of their speeds.

STEP 3

Define variables for the speeds of the two cars. Let v1 v_1 v1​ be the speed of the slower car and v2 v_2 v2​ be the speed of the faster car.

STEP 4

Express the relationship between the speeds using the given percentage. Since one car is 20% faster, we have:v2=v1+0.2v1 v_2 = v_1 + 0.2v_1 v2​=v1​+0.2v1​ v2=1.2v1 v_2 = 1.2v_1 v2​=1.2v1​

STEP 5

Calculate the speed of the second car. Given that v1=60 v_1 = 60 v1​=60 km/h, substitute into the equation:v2=1.2×60 v_2 = 1.2 \times 60 v2​=1.2×60 v2=72 km/h v_2 = 72 \text{ km/h} v2​=72 km/h

STEP 6

Determine the ratio of their speeds. The ratio of the speeds v1:v2 v_1 : v_2 v1​:v2​ is:v1v2=6072 \frac{v_1}{v_2} = \frac{60}{72} v2​v1​​=7260​Simplify the ratio:6072=56 \frac{60}{72} = \frac{5}{6} 7260​=65​Thus, the ratio of their speeds is 56 \boxed{\frac{5}{6}} 65​​.

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1. One car is 20% faster than the other car.
2. We need to find the ratio of their speeds.
3. One car's speed is given as 60 km/h.
4. We need to find the speed of the other car.

1. Define variables for the speeds of the two cars.
2. Express the relationship between the speeds using the given percentage.
3. Calculate the speed of the second car.
4. Determine the ratio of their speeds.

Define variables for the speeds of the two cars. Let $v_1$ be the speed of the slower car and $v_2$ be the speed of the faster car.

Express the relationship between the speeds using the given percentage. Since one car is 20% faster, we have:
$v_2 = v_1 + 0.2v_1$ $v_2 = 1.2v_1$

Calculate the speed of the second car. Given that $v_1 = 60$ km/h, substitute into the equation:
$v_2 = 1.2 \times 60$ $v_2 = 72 \text{ km/h}$

Determine the ratio of their speeds. The ratio of the speeds $v_1 : v_2$ is:
$\frac{v_1}{v_2} = \frac{60}{72}$
Simplify the ratio:
$\frac{60}{72} = \frac{5}{6}$
Thus, the ratio of their speeds is $\boxed{\frac{5}{6}}$ .