Algebra

posted by .

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?

• Algebra -

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~ :)

• Algebra -

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