Respuesta :
To find the rate of the eastbound train, we proceed as follows:
Step 1: We make a sketch of the two trains and their direction of travel
Step 2: We label the diagram with the speed of travel of each train
Given that the eastbound train travels 10 miles per hour slower than the westbound train, then:
Speed of eastbound train = speed of westbound train - 10 miles/hour
If we represent the speed of the westbound train as w, then:
Speed of eastbound train = w - 10 miles/hour
OR
Speed of eastbound train = w - 10
Now, see the diagram below:
Step 3: We write out the rate-distance formula, as follows:
[tex]Dis\tan ce=Rate\text{ }\times time[/tex]Step 4: We apply the rate-distance formula as follows:
Given that after a period of time of 3 hours , the two trains are a distance of 570 miles apart, we can say that:
Distance = 570 miles
Time = 3 hrs
Now, since the two trains are travelling in opposite directions, the overall rate of their relative motion is:
Rate = rate of eastbound train + rate of westbound train
Thus:
Rate = (w - 10) + w
Rate = (2w - 10) miles/hour
Now, substitute for rate, distance and time in the rate-distance formula;
[tex]\begin{gathered} Dis\tan ce=Rate\text{ }\times time \\ 570=(2w-10)\times3 \end{gathered}[/tex]Step 5: We solve the resulting equation for w, as follows:
[tex]\begin{gathered} 570=(2w-10)\times3 \\ 570=(2w\times3)-(10\times3) \\ 570=6w-30 \\ 570+30=6w \\ 600=6w \\ \frac{600}{6}=w \\ 100=w \\ w=100\text{ miles/hour} \end{gathered}[/tex]Thus, w = 100 miles/hour
Step 6: We now solve for the rate (speed) of the eastbound train, as follows:
Since:
Speed of eastbound train = w - 10 miles/hour
And w = 100miles/hour, we have that:
Speed of eastbound train = (100 - 10)miles/hour
Speed of eastbound train = 90 miles/hour
Therefore, the rate (or speed) of the eastbound train is 90 miles/hour

