MOTION PROBLEM INVOLVING LINEAR EQUATIONS IN ONE VARIABLE

Two jeepneys starting from the same place and traveling in opposite directions are 528 kilometers apart in 6 hours. One rate is 7 kilometers per hour faster than the other rate. Find the rate of each.
 
Solution:
 
Let x = rate of one jeepney
x + 7 = rate of the other jeepney
 
Based from the distance formula, D = rt, where D is the distance, r is the rate and t is the time, then
 
6x + 6(x + 7) = 528                    ] equation
6x + 6x + 42 = 528
12x = 528 - 42
12x = 486
12      12
 
x = 40.5 kms per hour             ] speed of one jeepney
x + 7 = 47.5 kms per hour      ] speed of the other jeepney
 
Hence, one jeepney was traveling at 40.5 km/hr while the other jeepney was traveling at 47.5 km/hr.
 
Check:
 
6(40.5) + 6(40.5 + 7) = 528
243 + 6(47.5) = 528
243 + 285 = 528
528 = 528