Question

Please Help

Teresa and Holly are both traveling to the mountains over the break. Teresa makes a 1.5 mile detour to get gas and lunch. The total number of miles Teresa drives can be modeled by the function T=75h+1.5. Holly makes a 5-mile detour to drop her dog off with a dog sitter. The total number of miles Holly drives can be modeled by the function H=65h+5. If h represents the number of hours after each girl leaves their home, which statement best compares Holly's speed to Teresa's speed?

Holly's speed is _____ (3.5,5,10,60,74.5) miles_____(slower,faster) than Teresa's.

Answer 1

Explanation:

To compare Holly's speed to Teresa's, we need to find the rate at which each girl is driving, which is given by the coefficients of h in their respective functions.

In Teresa's case, her function is T = 75h + 1.5, where T represents the total number of miles Teresa drives and h represents the number of hours after she leaves home. The coefficient of h is 75, which means Teresa is driving at a rate of 75 miles per hour.

In Holly's case, her function is H = 65h + 5, where H represents the total number of miles Holly drives. The coefficient of h is 65, which means Holly is driving at a rate of 65 miles per hour.

To compare their speeds, we can look at the coefficients directly. Since 75 is greater than 65, this means that Teresa is driving faster than Holly.

Therefore, the statement that best compares Holly's speed to Teresa's is: Holly's speed is slower than Teresa's.