rain A covers 200 km in 30 minutes less time than train B. Train B travels 20km/h slower than train A.An equation which could be used to solve for b, the speed of train B, is: Responses
Question
rain A covers 200 km in 30 minutes less time than train B. Train B travels 20km/h slower than train A.An equation which could be used to solve for b, the speed of train B, is: Responses
Solution
The first step is to understand the problem. We know that train A covers 200 km in 30 minutes less time than train B. We also know that train B travels 20km/h slower than train A. We are asked to find an equation that could be used to solve for b, the speed of train B.
Let's denote:
- the speed of train A as a (in km/h),
- the speed of train B as b (in km/h),
- the time it takes for train A to cover 200 km as t1 (in hours),
- the time it takes for train B to cover 200 km as t2 (in hours).
From the problem, we have the following relationships:
- a = b + 20 (since train A travels 20km/h faster than train B),
- t1 = t2 - 0.5 (since train A takes 30 minutes, or 0.5 hours, less than train B to cover the same distance),
- 200 = a * t1 (distance = speed * time for train A),
- 200 = b * t2 (distance = speed * time for train B).
We can substitute (1) into (3) and (2) into (4) to get two equations in terms of b: 3') 200 = (b + 20) * t1, 4') 200 = b * (t1 + 0.5).
We can solve these two equations simultaneously to find the value of b.
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