SOLUTION: 1. Thomas left Miami and drove at a speed of 41 mph. Katherine left 1 hour and 28 minutes later and drove at a speed of 57 mph. How long will it take Katherine to catch up with Tho

Question 87389: 1. Thomas left Miami and drove at a speed of 41 mph. Katherine left 1 hour and 28 minutes later and drove at a speed of 57 mph. How long will it take Katherine to catch up with Thomas?
2. EdHelper Airlines flight H3488 from Boston to Dallas averaged a speed of 90 mph more than the return trip back to Boston. The return trip took 1 109/308 times longer than the trip going to Dallas. The distance between Boston and Dallas is one thousand, seven hundred fifty miles. What was the average speed from Dallas to Boston?
Found 2 solutions by Flake, ankor@dixie-net.com:
Answer by Flake(45) (Show Source): You can put this solution on YOUR website!
1. Thomas left Miami and drove at a speed of 41 mph. Katherine left 1 hour and 28 minutes later and drove at a speed of 57 mph. How long will it take Katherine to catch up with Thomas?
----Step#1: try to visualize the problem. Drawing may help.
Basically it is asking at what point is Katherines distance equal to Thomas.
Drawing example:
|==============================> Thomas's distance is 41*Time
|**************************> Katherine's distance is 57*(Time-1hr 28min)
So, 57*(T-88/60) = 41T
57T-83.6 = 41T
16T = 83.6
T = 5.225hr = 5hr 13.5min
So, it took Katherine (5hr 13.5min) - (1hr 28min) = 3hr 45.5min
---------------------------------
2. EdHelper Airlines flight H3488 from Boston to Dallas averaged a speed of 90 mph more than the return trip back to Boston. The return trip took 1 109/308 times longer than the trip going to Dallas. The distance between Boston and Dallas is one thousand, seven hundred fifty miles. What was the average speed from Dallas to Boston?
---Step#1:List 2 conditions:
B-->D:
speed = 90+S
time =T
D-->B:
speed = S
time = (1 109/308)T
----Step#2: Distances are the same
so B-->D = D-->B
becomes (90+S)T = S(1 109/308)T ---Note the T's cancel out)
becomes 90+S = S(1 109/308)
becomes 90 = (109/308)S
becomes 90(308/109) = S
becomes S = 27720/109 --------(from your posting I'm not sure what the units are so not sure if it mph or km/hr)

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. Thomas left Miami and drove at a speed of 41 mph. Katherine left 1 hour and 28 minutes later and drove at a speed of 57 mph. How long will it take Katherine to catch up with Thomas?
:
Let t = amt of time for K to catch up with T:
:
Convert 28 min to hrs: 28/60 = .467, making K left 1.467 hrs after T
:
When K catches up we know they will have traveled the same distance, write a simple equation from this fact: Dist = Speed * time
:
K's dist = T's dist
57t = 41(t+1.467)
57t = 41t + 60.147
57t - 41t = 60.147
16t = 60.147
t = 60.147/16
t = 3.76 hrs which is 3 hrs 45.6 min, when K catches up with T
:
Check solutions by finding the distance both K & T have traveled
K: 57 * 3.76 = 214.3 mi
T: 41 * (3.76 + 1.467) = 214.3 mi also
:
:
2. EdHelper Airlines flight H3488 from Boston to Dallas averaged a speed of 90 mph more than the return trip back to Boston. The return trip took 1 109/308 times longer than the trip going to Dallas. The distance between Boston and Dallas is one thousand, seven hundred fifty miles. What was the average speed from Dallas to Boston?
:
Convert 1 109/308 to a decimal: 417/308 = 1.3539
:
Let s = Average speed from Dallas to Boston
Then:
(s+90) = Average speed from Boston to Dallas
:
Write a time equation Time = Dist/speed:
1.3539* =
=
Cross multiply:
2369.32s = 1750(s+90)
2369.32s - 1750x + 157500
619.32s = 157500
s = 157500/619.32
s = 254.3 mph Dallas to Boston
:
Check solution using speed and time
254.3 + 90 = 344.3 mph Boston to Dallas
1750/254.3 = 6.88 hrs
1750/344.3 = 5.08 hr
6.88/5.08 = 1.354 ~ 1 & 109/308

RELATED QUESTIONS
Devin left miami and drove at a speed of 45 mph. Timothy left 1 hour later and drove at a (answered by stanbon)
Alexander left Miami and drove at a speed of 50 mph. Jason left 2 hours later and drove... (answered by Alan3354)
Sandra left New York and drove at a speed of 20 kph. Cecille left 3 hours later, from the (answered by josmiceli)
Rachel left New York and drove at a speed of 50 mph. Brad left 3 hours later driving at... (answered by jorel1380)
Andrew left James' house and drove east at an average speed of 50 mph. Sam left one hour (answered by richwmiller)
At the end of spring break, Lucy left the beach and drove back towards home, driving at a (answered by josgarithmetic,ikleyn)
alberto left deshawn's house and drove toward the train station at an average speed of 65 (answered by Boreal)
A group of coworkers drove a car and a minivan to a conference. The car left first and... (answered by TimothyLamb)
Dan left the hospital and drove toward the train station at an average speed of 30 mph.... (answered by lwsshak3)