WyzAnt.comRob and Juanita are 7.7 miles apart. If they walk in the same direction Rob will reach Juanita in 11 hours. If they walk towards each other they meet in 1 hour. What speed are they walking.
I have a linear question
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2 Answers
------------------------------------------------------------------------->, rob's distance
----------------------------------->, juan's distance
<----------------J---------------->
--------------------><---------------
<---7.7-x---------><-------x------>
<---------------7.7 mi------------->
rob's distance juan's distance
We know both distances, and we know both times, so r = d/t
For rob: (7.7 + J)/11 = (7.7-x)/1 for juan: J/11 = x/1
Solve by substitution, x = 3.5 This is the distance juan walks toward rob. Juan' speed = 3.5 mph
7.7 - 3.5 = 4.2 Robs speed = 4.2 mph
If two objects are moving toward to each other (or in the opposite directions), the velocity of convergence (or breakaway) is the sum of their individual velocities. d = (v1 + v2)*t (d - distance in miles, t - time in hours) ....... (1)
If the objects are moving in the same direction, then the velocity of convergence (or breakaway) is equal to the difference between their individual velocities. d = (v1 - v2)*t ........(2)
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Let's assume that Rob's velocity is vR and Juanita's velocity is vJ .
(1) If they walk towards each other they meet in 1 hour and distance they walked is 7.7 mi ------> (vR + vJ) * 1 = 7.7 ------> vR + vj = 7.7 --------> vR = 7.7 - vJ........(3)
(2) If they walk in the same direction Rob will reach Juanita in 11 hours ------>
Rob's distance is (11 * vR)
— -------> 11( vR - vJ) = 7.7
Juanita's distance is (11 * vJ) ↓
7.7 ↓
11((7.7 - vJ) - vJ) = 7.7
11 11
7.7 - 2vJ = 0.7 ------>
-2vJ = -7 -------> vJ = 3.5 mph ------> (3) ------> vR = 7.7 - 3.5 = 4.2 mph
