A car went 346 miles in 6 hours, traveling part of the time at 55 miles per hour and part of the time at 65 miles per hour. How long did the car travel at each speed?

 The car traveled;

a)  for 4.4 hours with speed of 55 miles / hour

and

b) for  1.6 hours with speed of 65 miles / hour

Explanation:

Let the time taken by the car while moving with speed 55 miles per hour = x hours

Then remaining time  the car move at speed of 65 miles per hour is =6-x hours

using formula

S= V ×T

Where S= distance

V = speed

T = time

First case

S= ?

V=55 m/h

T= x hours

put values in formula above

==> S= V ×T

==> S1= 55 × x = 55 x miles

Second case

S=?

V= 65 m/h

T= ( 6-x ) hours

Putting values in formula above

S= V ×T

==> S2= 65 × (6-x) =65(6-x) miles

Total distance covered by the car = S1+S2=55x+65(6-x)

=  55x+ 390-65x

= -10x+390  miles

But total distance given is 346 miles

==> -10x+390=346

==> -10x=346-390

==>  -10x =  -44

==> x=44/10=4.4 hours

So, car traveled for 4.4 hours with speed of 55 miles / hour and for  1.6 hours with speed of 65 miles / hour

it about 600 mph from what i calculated

one person pulls 90n one way and the other has 100n pulling the other way.

so the net force = 90 - 100 = -10n,

or the ans can be 10n if the picture shows -90n and 100n instead.