Final answer:
The distance will increase by 44% if both the speed and time are increased by 20%, since distance is the product of speed and time and both factors would be multiplied by 1.20, resulting in a new distance of 1.44 times the original.
Step-by-step explanation:
When considering the increase of both speed and time by 20%, we first have to understand that distance is the product of speed and time. Mathematically, this is represented as distance = speed × time. In the context of this problem, if both the speed and time increase by 20%, they individually become 1.20 times their original value.
To find the percent increase in distance, we calculate the new distance after the increase:
New speed = 1.20 × original speed
New time = 1.20 × original time
New distance = New speed × New time = (1.20 × original speed) × (1.20 × original time) = 1.20 × 1.20 × (original speed × original time) = 1.44 × original distance
Therefore, the new distance is 144% of the original distance. To find the percent increase, we subtract 100% from this amount:
Percent increase in distance = 144% - 100% = 44%
The distance will increase by 44% if the speed and time both increase by 20%.