# Brain Thinkers

• Nov 24th 2008, 09:45 PM
not happy jan
Brain Thinkers
Could I please have some help with these 2 questions?
1. In a maths competition with 15 questions, 6 marks are given for each correct answer, 0 marks for each wrong answer and 3 marks for no answer. Bill scored 51 points in the competition. What is the greatest number of wrong answers he could have had.
2. A bi-athlete travels 30km in 2.25 hrs. She cycles part of the way at 20 km/h and runs the rest at 8 km/h. How far did she run?
• Nov 25th 2008, 07:12 AM
masters
Quote:

Originally Posted by not happy jan
Could I please have some help with these 2 questions?
1. In a maths competition with 15 questions, 6 marks are given for each correct answer, 0 marks for each wrong answer and 3 marks for no answer. Bill scored 51 points in the competition. What is the greatest number of wrong answers he could have had.
2. A bi-athlete travels 30km in 2.25 hrs. She cycles part of the way at 20 km/h and runs the rest at 8 km/h. How far did she run?

(2) Let t = #hrs cycling

Let 2.25 - t = #hrs running

Total distance = 30 km

D = rt

Distance is constant at 30

20(t) + 8(2.25 - t) = 30

20t - 8t + 18 = 30

12t = 12

t = 1 hours cycling

Number of hours spent running = 2.25 - 1 = 1.25 hours running

D = 8(1.25) = 10 km running

D = 20(1) = 20 km cycling
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Total = 30 km
• Nov 25th 2008, 08:00 AM
Soroban
Hello, not happy jan!

Quote:

2. A bi-athlete travels 30km in 2.25 hrs.
She cycles part of the way at 20 km/h and runs the rest at 8 km/h.
How far did she run?

We will use: . $\text{Distance} \:=\:\text{Speed} \times \text{Time} \quad\Rightarrow\quad T \:=\:\frac{D}{S}$

Let $x$ = distance she ran.
Then $30-x$ = distance she cycled.

She ran $x$ km at 8 km/hr.
. . This took her: . $\frac{x}{8}$ hours.

She cycled $30-x$ km at 20 km/hr.
. . This took her: . $\frac{30-x}{20}$ hours.

Her total time was $2\tfrac{1}{4}$ hours.

There is our equation! . . . $\frac{x}{8} + \frac{30-x}{20} \:=\:\frac{9}{4}$