Two motorcycles leave home at the same time, heading directly toward each other. they are a total of 196 miles apart. the first motorcycle travels at 65 miles per hour. the second motorcycle travels at 75 miles per hour. how long will it take for the two motorcycles to meet?

The time taken for the two motorcycles to meet is 1.4 hours or 84 minutes.

Let the time taken for the two motorcycles to meet be represented by t.

The formula for distance is denoted as:

For the first motorcycle, the distance will be:

= Speed × Time

= 65 × t

= 65t

For the second motorcycle, the distance will be:

= Speed × Time

= 75 × t

= 75t

Since they are a total of 196 miles apart, then the time taken for the two motorcycles to meet will be:

(65t + 75t) = 196

140t = 196

t = 196/140

t = 1.4 hours or 84 minutes

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Let the two motorcycles meet in T hours after their start of journey.

Given : First motorcycle travels at a speed of 65 miles per hour

 First motorcycle travels a distance of 65 miles in one hour

 First motorcycle travels a distance of (65 × T) miles in T hours

Given : Second motorcycle travels at a speed of 75 miles per hour

 Second motorcycle travels a distance of 75 miles in one hour

 Second motorcycle travels a distance of (75 × T) miles in T hours

Given : Before the journey began, Two motorcycles are 196 miles apart

We assumed that the two motorcycles meet in T hours after their start of journey. As the Distance between two motorcycles is 196 miles, The Distance covered by first motorcycle before it meets the second motorcycle and The Distance covered by second motorcycle before it meets the first motorcycle should be equal to 196 miles.

It means : Distance covered by first motorcycle in T hours and Distance covered by second motorcycle in T hours should be equal to 196

 (65 × T) + (75 × T) = 196

 65T + 75T = 196

 140T = 196

Answer : It takes 1.4 hours (84 mins) for the two motorcycles to meet

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