Question

The car is moving at a constant rate. By what percent of the distance increase if the speed is increased by 20% and the time is increased by 50%?

Answer 1

To calculate the percent increase in distance when the speed is increased by 20% and the time is increased by 50%, we can use the formula: Percent increase = (New distance - Original distance) / Original distance x 100. The percent increase in distance is 80% when the speed is increased by 20% and the time is increased by 50%.

Step-by-step explanation:

To calculate the percent increase in distance when the speed is increased by 20% and the time is increased by 50%, we can use the formula:

Percent increase = (New distance - Original distance) / Original distance x 100

Let's say the original distance is represented by 'd'. When the speed is increased by 20%, the new speed becomes 1.2 times the original speed. Similarly, when the time is increased by 50%, the new time becomes 1.5 times the original time. Therefore, the new distance is given by:

New distance = new speed x new time = 1.2 x d x 1.5

Now we can substitute these values into the percentage increase formula:

Percent increase = (1.2 x d x 1.5 - d) / d x 100

Simplifying the expression, we get:

Percent increase = (1.8d - d) / d x 100

which simplifies further to:

Percent increase = 0.8d / d x 100

Finally, cancelling out the 'd' terms and multiplying by 100, we find that the percent increase in distance is 80% when the speed is increased by 20% and the time is increased by 50%.

Answer 2

If the speed of a car is increased by 20% and the time is increased by 50%, the distance traveled increases by 80%.

Step-by-step explanation:

To determine by what percent the distance increases if the speed is increased by 20% and the time is increased by 50%, we can use the basic equation for distance traveled: distance (d) = speed (v) × time (t). If the original speed is v, then an increase by 20% gives us a new speed of 1.20v. If the original time is t, then an increase by 50% gives us a new time of 1.50t.

Original distance can be represented as d = v × t. The new distance after increasing the speed and time would then be d' = (1.20v) × (1.50t), which simplifies to d' = 1.80 × (v × t). This means the new distance is 1.80 times the original distance, which is an 80% increase.

To find the percentage increase, you would calculate ((d' - d) / d) × 100% which simplifies to ((1.80 - 1) × 100%) = 80%. Therefore, the distance increases by 80% when the speed is increased by 20% and the time is increased by 50%.