Speed question. please help

My old Holden’s speedometer was not calibrated correctly it displayed70 km/h when its true speed was 55 km/h, it also displayed 40 km/h whenits true speed was 32 km/h.

(a) Using the variables T for true speed and D for displayed speed, determine the linear equation that could relate the displayed and true speeds.

(b) When the speedometer displays 100 km/h how fast am I actually going?

(c) When I am going 100 km/h what speed does the speedometer display?

Re: Speed question. please help

A general linear equation that relates T and D is T = aD + b for some constants a and b. Substitute the two given pairs of values of T and D into that equation, and you'll get two equations in a and b.

Re: Speed question. please help

hi thanks for the reply.

so with your advice for

a) I plug in the values into the formula T = aD + b

55 = a70 + b and

32 = a40 + b

and how to I go solving for both of these? thanks

Re: Speed question. please help

Quote:

Originally Posted by

**mathkid182** 55 = a70 + b and

32 = a40 + b

and how to I go solving for both of these?

The equations are correct. Subtract the second equation from the first one; this eliminates b and leaves one equation in a only. Find a and then substitute it into any of the original equation to get an equation in b only.

For more on solving systems of linear equations, see, e.g., here.

Re: Speed question. please help

hi Emakarov,

thanks for the help. im trying to subtract the second equation from the first one however am having trouble of where to start, would you be able to show where the starting point please?

Re: Speed question. please help

so i think i did it and got a = 23/30 and b = 4/3 is this right? and with this info how do i answer the questions?thanks!

Re: Speed question. please help

Quote:

Originally Posted by

**mathkid182** so i think i did it and got a = 23/30 and b = 4/3 is this right?

Yes, this is correct.

Quote:

Originally Posted by

**mathkid182** and with this info how do i answer the questions?

Do you still remember what a and b denote? Re-read post #2. Once you have the equation, what is T when D = 100? What is D when T = 100?