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The Tomato and the Bean

Age 5 to 7 Challenge Level:

Tom's Dad sowed some tomato seed in February. He gave Tom one of the tomato plants in a pot.

At the beginning of May, Tom put his tomato plant outside. On the same day he sowed a bean in another pot.

Ten days later the bean plant was just $1$ cm (centimetre) above the soil surface. Tom measured his tomato plant which was already $38$ cm tall.

Each evening Tom measured his two plants.

On the evening of the next day the little bean plant had grown another $2$ cm so it was $3$ cm high. Each day it continued to grow double the amount it had grown the day before.

The tomato plant grew at a steady $5$ cm a day.


After how many days were the two plants the same height when Tom measured them in the evening? How high were they?