Step by Step

Number Theory Level 1

Rose and Mary begin to climb a staircase of 100 steps at the same time.

Rose climbs 10 steps in 15 seconds.

Mary climbs 10 steps in 20 seconds.

When one of then get the top, how much longer (in seconds) will it take the other to reach the top?

30 45 60 50

4 solutions

Sophie Crane
Apr 17, 2014

5 seconds are gained for every 10 steps. 100/10=10 and 10*5=50

Anubhav Sharma
Apr 5, 2014

Here,

one climbs 10 steps in 15 seconds

10 steps ============> 15 seconds

or, 1 step============> 15 / 10 seconds

or, 1 step ============> 1.5 seconds

or, 100 steps ============> $1.5\times 100$

So, 100 steps============> 150 seconds

Similarly,

other climbs 10 steps in 20 seconds

10 steps ============> 20 seconds

or, 1 step============> 20 / 10 seconds

or, 1 step ============> 2 seconds

or, 100 steps ============> $2\times 100$

So, 100 steps============> 200 seconds

Now, the difference is 200 - 150 = 50

thank u soo much

Raj Kumar - 6 years, 10 months ago

Giorgio de Fornasari
Sep 10, 2015

Rose gets the top in (15 x 10) = 150 seconds.

In that same time Mary has climbed (150 / 20) * 10 = 75 steps.

75 are the 3/4 of 100 so Mary needs (150/3) = 50 more seconds to reach the top

Rahma Anggraeni
May 20, 2014

$20 \times 10-15 \times 10$

$200-150$

$\boxed{50}$