A train travels at an average of 100 miles per hour for 4.5 hours and then travels at a speed of 140 miles per hour for 2.5 hours. How far did the car travel in the entire 7 hours?

720 miles

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750 miles

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810 miles

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780 miles

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800 miles

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Solution

The correct option is E
800 miles

$S p e e d_{1}$ = 100 miles/hour

$T i m e_{1}$ =4.5hour = $\frac{9}{2}$ hours

$D i s t a n c e_{1}$ = $S p e e d_{1}$ $\times$ $T i m e_{1} = 100$ $\times$ $\frac{9}{2}$ = 50 $\times$ 9 = 450miles

$S p e e d_{2}$ = 140 miles/hour

$T i m e_{2}$ =2.5hour = $\frac{5}{2}$ hours

$D i s t a n c e_{2}$ = $S p e e d_{2}$ $\times$ $T i m e_{2}$ =140 $\times$ $\frac{5}{2}$ = 70 $\times$ 5 = 350miles

$∴$ Total Distance = $D i s t a n c e_{1}$ + $D i s t a n c e_{2}$ = 450+350 = 800miles

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