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How long did James travel before Julio caught up with him?

James left the hardware store and traveled toward the capital at an average speed of 28 km/h.  Some time later Julio left traveling in the same direction but at an average speed of 35 km/h.  After traveling for four hours Julio caught up with James.

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Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (7 lesson ratings) (7)
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distance=rate x time
distances are the same
let t=James's time
28*t=35*4
28t=140
t=140/28=5 hours
 
Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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The distance James traveled = the catch up distance by Julio = (35-28)*4 = 28 km
So, James traveled 28/28 + 4  = 5 hours before Julio caught up with him.
William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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Julio: (35 km/hr)*(4 hr)  = 140 km
 
James (28 km/hr)*t = 140 km
 
t = (140 km)/(28 km/hr) = 5 hours
 
 
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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Hi Samantha;
James=28 km/h; (4+x) hours
Julio=35 km/h; 4 hours
 
 
Our first priority is to check for consistency of units.  For example, is any information provided in minutes or miles.  Everything is consistent, in kilometers and hours, so we may proceed.
 
We know that both men traveled the same distance when Julio caught up with James.
 
(28 km/hour)[(4+x)hours]=(35 km/hour)(4 hours)
Let's cancel units where appropriate...
(28 km/hour)[(4+x)hours]=(35 km/hour)(4 hours)
Let's proceed to cancel units where appropriate...
(28 km)(4+x)=(35 km)(4)
28(4+x)=35(4)
Cancelling units is always your first priority, before calculations.  This is because if the units are not aligned, you are working with the wrong equation.
112+28x=140
Let's subtract 112 from both sides as we proceed to isolate x...
28x=140-112
28x=28
x=1
 
James traveled 1 hour + 4 hours=5 hours