10. Mary's travel time and speed vary INVERSELY. Mary drives home from work in 40 minutes driving 55 mph. If Mary needs to get home in 35 minutes, how fast does she need to drive? (Rounded to the nearest whole number!)
time = constant / speed
t = k/s
40 = k / 55
k = 2200
so
t = 2200 / s
35 = 2200 / s
s = 2200/35 = 62.86 or 63 mph
distance = rate x time
d = 55 mph x (40/60) = 36.6 miles to her house.
Then 36.6 = rate x (35/60) so rate = 36.6 x 60/35 = ? mph
To determine how fast Mary needs to drive in order to get home in 35 minutes, we need to understand the relationship between her travel time and speed. The question states that Mary's travel time and speed vary inversely. This means that as her speed increases, her travel time decreases, and vice versa.
We can use the inverse variation formula to solve this problem. The formula is:
Speed × Time = Constant
Let's assign variables to the given values:
Mary's initial speed = 55 mph
Mary's initial travel time = 40 minutes
Mary's desired travel time = 35 minutes
We can set up the equation using the inverse variation formula:
Initial speed × Initial travel time = Desired speed × Desired travel time
Plugging in the values we know, we get:
55 mph × 40 minutes = Desired speed × 35 minutes
Now, we can solve for the desired speed:
(55 × 40) / 35 = Desired speed
Calculating this, we get:
(2200) / 35 ≈ 62.86
Rounded to the nearest whole number, Mary needs to drive approximately 63 mph in order to get home in 35 minutes.