motion problems?

Question

Can anyone help me with this math problem. It would be helpful if it was step by step I have more of them. PLEASE
Chris and Leslie drove a total of 893 miles in 18 hours. Chris drove the first part of the trip and average 55 miles per hour. Leslie drove the rest of the trip and average of 45 miles per hour. For what length of time did Chris drive?

Answer 1

This is an example of simultaneous equations, that is, using 2 equations with 2 variables.



Let x = # hours that Chris drove

Let y = # hours that Leslie drove

We know they both drove for a total of 18 hours, so the first equation will be:



x + y = 18 hours



We also know that the number of hours Chris drove, at 55 mph plus the total miles driven by Leslie, at 45 mph equals the number of total miles. The second equation will be:



55x + 45y = 893



Our two equations then, are:



x + y = 18

55x + 45y = 893



Using the first equation, solve for the variable that represents Chris, which is x.



x = 18 - y



Now plug this value for x into the second equation:



55(18-y) + 45y = 893



990 - 55y + 45y = 893



990 - 893 = 55y - 45y

97 = 10y

9.7 = y



Take this value for Leslie's driving time, and plug it into the original equation, like so:



9.7hours + x = 18 hours

x = 8.3 hours = Chris' driving time

Answer 2

So, as a team,

d = 893 miles

t = 18 hrs



we know this eqtn: average speed = d/t

using c and l as subscripts to designate Chris and Leslie,



Chris: dc = 55 * tc

Leslie = dl = 45 * tl



t = 18 = tc + tl

d = 893 = dc + dl so together,



d = 55*tc + 45*tl

d = 55*tc + 45*(t-tc)

893 = 55*tc + 45*(18 - tc)

893 = 55*tc + 810 - 45*tc

893 = 10*tc + 810

83 = 10*tc

8.3 = tc

Answer 3

Speed:

v = s/t

t = s/v



Chris drives for x hours:

x = s/55



Leslie drives for y hours:

y = (893-s)/45



However:

t = x+y

18 = s/55 + (893-s)/45

18*55 = s + 55(893-s)/45

990 = s + (49115-55s)/45

45*990 = 45s - 55s + 49115

44550 = -10s + 49115

10s = 4565

s = 456.5



Chris drives for x hours:

x = s/55

x = 456.5/55



x = 8.3



Answer: Chris drove for 8.3 hours.



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Answer 4

chris drove an average of 55m/h.

the total distance drove by chris is

893x55/100=491.15miles.

the time taken by chris to drive 491.15 miles is

491.15/55=8.93hours.



thus chris took 8 hours 55minutes and 48 seconds.

Answer 5

let chris drive for x hrs and leslie for y hrs

the equations are

x+y=18

(55x+45y)=893

45x+45y=810

10x=83

x=8.3

y=9.7

chris drove for 8 hrs 18 min