Solving the Puzzle: Speed of Two Buses

[gunslinger]

Homework Statement

A bus travels 650km in 3 hours less than the other bus whose speed is 15 km/h slower than the speed of the first bus.

A. Assemble the equation.
B. Solve the equation and state the speeds of the buses.

Homework Equations

The Attempt at a Solution

V = d / t
Velocity of the first bus = Velocity of the second bus - 15; V1 = 650 / t2 - 3
Time of the first bus = Time of the second bus - 3; V1 - 15 = 650 / t1 + 3

I don't really know.

 

[gunslinger]

I'm not even sure If I can use physics equations in a mathematics exam

 

[Dick]

I'm not even sure If I can use physics equations in a mathematics exam

Of course you can use v=d/t. I think you are just getting confused with all the variables. Just pick one. Let t be the time of the faster bus. Now write the velocity relation just using the variable t.

 

[haruspex]

V1 = 650 / t2 - 3

Pls use enough parentheses to avoid confusion.

Time of the first bus = Time of the second bus - 3; V1 - 15 = 650 / t1 + 3

You'll do better if you write the second equation using the same two unknowns.

 

[Ray Vickson]

Homework Statement

A bus travels 650km in 3 hours less than the other bus whose speed is 15 km/h slower than the speed of the first bus.

A. Assemble the equation.
B. Solve the equation and state the speeds of the buses.

Homework Equations

The Attempt at a Solution

V = d / t
Velocity of the first bus = Velocity of the second bus - 15; V1 = 650 / t2 - 3
Time of the first bus = Time of the second bus - 3; V1 - 15 = 650 / t1 + 3

I don't really know.

Either use a single t, or else use the two of them properly, as in:
$$V_1 = 650/t_1\\ V_1 - 15 = 650/t_2\\ t_2 = t_1 + 3$$
You will have three unknowns $V_1, t_1, t_2$ and three equations, so you ought to be able to solve. Your blunder was to put $t_2-3$ in the first equation and $t_1 + 3$ in the second equation, but never specifying what is the relation between $t_1$ and $t_2$.

BTW: if you do insist on putting the +3 and -3 in your two equation, you need to write them properly. What you wrote means, literally,
$$V_1 = \frac{650}{t_2} - 3.$$ If you mean
$$V_1 = \frac{650}{t_2 - 3}$$ then you need to use parentheses, like this:
V1 = 650/(t2-3). Do you see the difference?

 

[Joffan]

While the advice above is reasonable, I think we're skipping steps here.

There are FOUR equations in FOUR unknowns to start with. The four unknowns are $t_1, v_1, t_2, v_2$ for the time and velocity of the two buses on the 650km journey.

One of the equations is
$$t_1v_1 = 650$$
... find the other three equations.

Then we can reduce the system to TWO equations in TWO unknowns by substitution.

Then we will be able to reduce to a quadratic equation in one unknown.