Question 174165
For both trains, the same formula applies, but I'll write it
differently for each train so I keep track of each train's data
{{{d = r*t}}}
{{{d}}}=distance in miles
{{{r}}}= speed in mi/hr
{{{t}}}= elapsed time in hrs
For train a:
{{{d[a] = r[a]*t[a]}}}
For train b:
{{{d[b] = r[b]*t[b]}}}
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Given:
{{{r[a] = 35}}} mi/hr
{{{r[b] = 45}}} mi/hr
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I want to have
the start time for both trains the same, at 7 AM, 
so I want to know how far train a has gone between
5 AM and 7 AM
{{{d = 35*2}}}
{{{d = 70}}} mi
Now the trains will both travel for 1 hr, 7 AM to 8 AM
{{{d[a] = r[a]*t[a]}}}
{{{d[a] = 35*1}}}
{{{d[a] = 35}}}mi
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{{{d[b] = r[b]*t[b]}}}
{{{s[b] = 45*1}}}
{{{d[b] = 45}}}mi
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{{{d[b] - d[a] = 45 - 35}}}
{{{d[b] - d[a] = 10}}}mi
So, train b has gained 10 mi on train a, but train a
already had a 70 mi head start on train b
{{{70 - 10 = 60}}}
Train a is 60 mi ahead of train b
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check answer:
For train a:
{{{d[a] = r[a]*t[a]}}}
{{{d[a] = 35*3}}}
{{{d[a] = 105}}}mi
For train b:
{{{d[b] = r[b]*t[b]}}}
{{{d[b] = 45*1}}}
{{{d[b] = 45}}}mi
The difference is 60 mi