Standing on the Table
Clement and Dmitri both measure how much taller they are than the other when standing on a table. Can you work out how tall the table is?
Age
11 to 14
Challenge level
Problem
When Clement stands on a table and Dmitri stands on the floor, Clement is $80\text{cm}$ taller than Dmitri. When Dmitri stands on the table and Clement stands on the floor, Dmitri is $1\text{m}$ taller than Clement.
How tall is the table?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: $90$ cm
Dmitri is $d$ centimetres tall, Clement is $c$ centimetres tall and the table is $t$ centimetres tall.
The information in the question tells us that:
$c+t=d+80$
$d+t=c+100$
$d+t=c+100$
Then add these two equations together, which gives:
$c+d+2t = c+d+180$
Subtracting $c+d$ from both sides gives:
$2t=180$
Dividing by $2$ gives:
$t=90$
Therefore the table is $90\text{cm}$ tall.