Maria leaves her house to meet jane at the zoo. Jane lives further away than Maria and drives 8mph fatser than Maria. Their combined distance is 84 miles. If they both drive 45 minutes, find their average speeds.
dm= distanance maria
dj=distance jane
84=dm+dj
dm=(speedjane+8)3/4
dj= speedjane*3/4
84=3/4(speedjane+8)+3/4speedjane
solve for speed jane first. Maria adds 8
To find their average speeds, we need to determine their individual speeds first. Let's assume that Maria's speed is "x" mph. Since Jane drives 8 mph faster than Maria, her speed will be "x + 8" mph.
We are given that they both drive for 45 minutes, which is equivalent to 0.75 hours.
Now, let's use the distance formula: distance = speed × time.
The distance Maria covers (d1) can be calculated as:
d1 = x × 0.75
Similarly, the distance Jane covers (d2) can be calculated as:
d2 = (x + 8) × 0.75
We know that their combined distance is 84 miles, so we can set up the equation:
d1 + d2 = 84
Substituting the values we calculated earlier, we have:
(x × 0.75) + ((x + 8) × 0.75) = 84
We can now solve this equation to find the value of x (Maria's speed).
0.75x + 0.75x + 6 = 84
1.5x = 78
x = 78 ÷ 1.5
x = 52
Therefore, Maria's speed is 52 mph. To find Jane's speed, we can simply add 8 mph to Maria's speed:
Jane's speed = Maria's speed + 8
Jane's speed = 52 + 8
Jane's speed = 60 mph
Finally, to calculate their average speeds, we find the mean of their individual speeds:
Average speed = (Maria's speed + Jane's speed) ÷ 2
Average speed = (52 + 60) ÷ 2
Average speed = 112 ÷ 2
Average speed = 56 mph
So, their average speeds are 56 mph.