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
[tex]:\implies[/tex] First motorcycle travels a distance of 65 miles in one hour
[tex]:\implies[/tex] First motorcycle travels a distance of (65 × T) miles in T hours
Given : Second motorcycle travels at a speed of 75 miles per hour
[tex]:\implies[/tex] Second motorcycle travels a distance of 75 miles in one hour
[tex]:\implies[/tex] 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
[tex]:\implies[/tex] (65 × T) + (75 × T) = 196
[tex]:\implies[/tex] 65T + 75T = 196
[tex]:\implies[/tex] 140T = 196
[tex]:\implies \mathsf{T = \dfrac{196}{140}}[/tex]
[tex]:\implies \mathsf{T = 1.4}[/tex]
Answer : It takes 1.4 hours (84 mins) for the two motorcycles to meet
