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Two buses leave the station at 4:00A.M., one travelling east at 60kph and

the other, west at 65kph. At what time will they be 50km apart?
Pls Include Represent, Relate, Equate, Solve and Prove. :DD

their combined speed is 125 km/hr

now, distance = speed * time

Did you know?

Did you know that using the concept of relative motion can help us solve problems like determining when two objects will be a certain distance apart? This can be illustrated by the following example: Two buses leave the station at 4:00 A.M. One bus travels east at a speed of 60 kph, while the other travels west at a speed of 65 kph. The question is, at what time will they be 50 km apart? To represent the situation, we consider the buses as two points moving on a horizontal number line, with one point moving towards the positive direction and the other towards the negative direction. To relate the variables, we can assign a common starting point (the station) and let time be the independent variable. We also need to consider the distance as the dependent variable, which is the key factor in determining when the buses will be 50 km apart. To equate the variables, we can use the total distance equation: distance = rate × time. For the bus travelling east, the equation is d1 = 60t, and for the bus travelling west, the equation is d2 = 65t. Here, d1 and d2 represent the distances covered by each bus, and t represents time. To solve the problem, we need to find the time at which the sum of the distances covered by the two buses equals 50 km. Thus, we have the equation 60t + 65t = 50, which simplifies to 125t = 50. To prove the solution, we solve for t: t = 50/125, which equals 0.4 hours. Since we are measuring time from 4:00 A.M., we can convert this to minutes by multiplying 0.4 by 60, which gives us 24 minutes. Therefore, the buses will be 50 km apart at 4:24 A.M. In conclusion, by representing, relating, equating, solving, and proving the problem using the concept of relative motion, we can determine when two objects, in this case, buses, will be a certain distance apart.