One driver drives 25 mph faster than another driver does. They start at the same time and after a certain amount of time, one driver has driven 90 miles, and the other driver has driven 165 miles. What are the speeds of the two drivers?

speed of slower driver 30 mph

speed of faster driver = 55 mph

Step-by-step explanation:

let the speed of slower driver b x mph

given

One driver drives 25 mph faster than another driver does

Speed of faster driver = (x+25) mph

we know time = speed / distance

also in same time faster will travel more distance than the slower one.

thus

driver with speed  (x+25) mph would have traveled 165 miles

driver with speed  x mph would have traveled 90 miles

time for driver with speed  (x+25) mph = 165/(x+25)

time for driver with speed  x mph = 90/x

Given that

They start at the same time and after a certain amount of time, one driver has driven 90 miles, and the other driver has driven 165 miles.

\time for driver with speed  (x+25) mph =time for driver with speed  x mph

165/(x+25) = 90/x

165x = 90(x+25)

=> 165x = 90x + 2250

=> 165x -90x = 2250

=> 75x = 2250

=> x = 2250/75= 30

Thus, speed of slower driver 30 mph

speed of faster driver = 30+25 = 55 mph

anser is a

step-by-step explanation:

negitive slope

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9