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Speed, distance, time problem

This is probably not that difficult but I think I'm trying to approach it the totally wrong way.

Driving along a crowded motorway, you notice that it takes a time t to go from one mile marker to the next. When you increase your speed by 8.5 miles per hour, the time to go one mile decreases by 15 seconds.

What was your original speed in miles per hour?
Reply 1
Avatar for Chaoslord
Chaoslord
16
a change of 8.5 mph causes a change of 15 seconds.

speed x time = distance

im gonna covert everything to miles per sec

u×t=1mileu \times t = 1 mile

(u+177200)(t−15)=1mile(u + \frac{17}{7200})(t - 15) = 1 mile

(u+177200)(t−15)=ut(u + \frac{17}{7200})(t - 15) = ut


ut+17t7200−17400−15u=utut + \frac{17t}{7200} - \frac{17}{400} -15u= ut


17t7200=17400+15u\frac{17t}{7200} = \frac{17}{400} + 15u


t=18+108000u17t = 18 + \frac{108000u}{17}


u18+108000u217=1mpsu18 + \frac{108000u^2}{17} = 1 mps


306u+108000u2=17306u + 108000u^2 = 17


(u+1712000)2−(1712000)2=17108000(u + \frac{17}{12000})^2 - (\frac{17}{12000})^2 = \frac{17}{108000}

i plugged it through cause its a bit messy

im getting 44.8?
Reply 2
Avatar for username74116
username74116
OP
When you were multiplying out the brackets you've forgot to multiply the two outside terms which give -15u.

Once that mistake is corrected you're still left with u and t so you can't solve it.

This was one of the methods I already tried.

Also the question does say a "crowded motorway" so 200mph does seem a little too fast.
Reply 3
Avatar for Chaoslord
Chaoslord
16
craighay1
When you were multiplying out the brackets you've forgot to multiply the two outside terms which give -15u.

Once that mistake is corrected you're still left with u and t so you can't solve it.

This was one of the methods I already tried.

Also the question does say a "crowded motorway" so 200mph does seem a little too fast.


oh i see, it can still be done

just rearrange the formula to get t = something u and sub into the ut = 1

should work
Reply 4
Avatar for Piricad
Piricad
Chaoslord
oh i see, it can still be done

just rearrange the formula to get t = something u and sub into the ut = 1

should work

33.8 mph
Reply 5
Avatar for Chaoslord
Chaoslord
16
Piricad
33.8 mph


i got 44.8 but i reckon i just typed in a number wrong

i think its clear this method works now =P

good luck! =P

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