Suzi drove home at 69 mph, but her brother Jim, who left at the same time, could drive at only 41 mph. When Suzi arrived, Jim still had 112 miles to go. How far did Suzi drive?
recall:
speed (v) is distance (d) travelled over a certain period of time (t), or
v = d/t
since Suzi is faster that Jim given their speeds, we can get the difference of their speeds:
69 - 41 = 28 mph
*this 28 mph only means that after 1 hour, the gap or distance between them is 28 miles, since v = d/t --> 28 = d/1 --> d = 28)
in the problem, it's said that the distance between them when Suzi arrived home is 112,, therefore:
v = d/t
28 = 112/t
t = 4 hours
since they left at the same time, Suzi drove for 4 hours, therefore:
v = d/t
69 = d/4
d = ?
now solve for d.
hope this helps~ :)
D = RT, T = D/R
69 = Suzi Rate
T = Suzi Time
69T = Suzi Distance
41 = Jim Rate
T + 2.73 = Jim Time (T = 112/41 = 2.73)
41(T + 2.73) = Jim Distance
Since distances are equal
69T = 41(T + 2.73)
69T = 41T + 111.93
28T = 111.93
T = 3.99 = 4
69T = Suzi Distance
69(4) = 276 miles
To find out how far Suzi drove, we can set up an equation based on the information given.
Let's assume the time it took for Suzi and Jim to drive is t hours.
Since Suzi drove at a speed of 69 mph, the distance she traveled is given by:
Distance = Speed x Time
Distance = 69 mph x t hours
Similarly, Jim drove at a speed of 41 mph, and the distance he traveled is given by:
Distance = Speed x Time
Distance = 41 mph x t hours
Now, we know that when Suzi arrived at her destination, Jim still had 112 miles to go. This means the distance Suzi traveled is equal to the total distance minus Jim's remaining distance:
Distance Suzi Drove = Total Distance - Jim's Remaining Distance
Distance Suzi Drove = (69 mph x t hours) - 112 miles
Since we don't know the exact time it took for Suzi and Jim to drive, we can't solve for the distance Suzi drove with this equation alone. We need more information to find a specific value for t or the total distance.
If there is any additional information available, please provide it so we can solve the problem.