Question 519623
Sharon Data
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Distance traveled = x
Speed = 8mph
Time taken to cover distance x = t
Distance = Speed * time
x=8*t

Rae Data
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Distance traveled = x
Speed = 10mph
Time taken to cover distance x = t-15 (Rae started 15 minutes later)
Distance = Speed * time
x=10*(t-15)

Since both will cover the same distance therefore

10(t-15)=8t
10t-150=8t
10t-8t=150
2t=150
t=150/2
t=75 minutes or 1.25 hours

After (75-15) 60 minutes of crossing the bridge Rea will catch up with Sharon at 1:33pm 
Check
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Sharon Data
Distance traveled = x
Speed = 8mph
Time taken to cover distance x = t = 1.25 hours
Distance = Speed * time
x=8*t= 8*1.25 = 10 miles

Rae Data
Distance traveled = x
Speed = 10mph
Time taken to cover distance x = t-15 = 75-15=60 minutes = 1 hour
Distance = Speed * time
x=10*1= 10 miles